{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-7jtqlF8YFU7"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import torch\n",
    "from utils.optim import Optim, output, w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "bt6sbhvuOzb-"
   },
   "source": [
    "# SGD Optimizer\n",
    "\n",
    "In this exercise we try to implement the vanilla SGD optimzation algorithm over a mini batch of data points. Recall that the equation for vanilla SGD was as follows:\n",
    "\n",
    "$$\n",
    "w_i = w_i - \\frac{\\partial{C}}{\\partial{w_i}} * lr\n",
    "$$\n",
    "\n",
    "Where $C$ is the cost function and $lr$ is the learning rate.\n",
    "\n",
    "In the below class, complete the ``` my_step()``` function, both $\\frac{\\partial{C}}{\\partial{w_i}}$ and $lr$ are given to you. \n",
    "\n",
    "Hint: You can access $w_i$ through ```p.data``` and can use the [``` x.add_```](https://pytorch.org/docs/stable/tensors.html?highlight=add_#torch.Tensor.add_) function to perform the addition inplace !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qL1hj2XLO9rx"
   },
   "outputs": [],
   "source": [
    "class SGDOptimizer(Optim):\n",
    "    def __init__(self, params, lr):\n",
    "        defaults = dict(lr=lr)\n",
    "        super(SGDOptimizer, self).__init__(params, defaults)\n",
    "\n",
    "    def my_step(self, p, state, group):\n",
    "        lr = group['lr']\n",
    "        d_p = p.grad.data\n",
    "        p.data.add_(-group['lr'], d_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "bnvBpqL8QY30"
   },
   "source": [
    "Once, that's done we can try to visualise how optimzation is taking place by optimizing over a quadratic function as shown in lecture.\n",
    "\n",
    "We see a lot of variance in the direction of the optimzation if we use a large learning rate and an inability to effectively minimise the function if we use a small learning rate !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 731
    },
    "colab_type": "code",
    "id": "p1gkP9nzb6ae",
    "outputId": "89319756-98cb-4163-cea1-498ab36d3926"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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No1kqDY0ucGbOaH48bE67eTRLpaHRBXTxydHt5umjvmhonDBoluo4oNrt5qnVK6lwuTilfwFXjB6DXqej3uvl0eVf4wwGuXnyVAalpfHKhnVUud0km8x8d9x4gtEo/1q1Am8oxPfGTyDH7jjSP+eYRxNVHCklvnAYTygUT0G84TC+cBhvKIQvvh+IRAhEIvgjsf1gJEowGlusGIxECasqoWiUiLpvaYZKVJVEVBVVqkSljC1SjG8PRojYCiudECg6wZ9nn8PkvLx2+57rcHD3tOkIIbjzs08IRaPodTqeXLmCBSeNwW408vy6NVw3fiLbGhu5dux4nl27muZAgNc2bmBsdg4mvZ43Nm3ihxMnYVSO/ITVY5njTlSqlLQEAjT5fTT5/TT7/TQH/DT7AziDAVoCseQKBnAFg63JEwq1eZK3hSIEFoMBk6LEVtjqFYyKEltnpSgYFB0WvQm9TodBia3eVXSxRYr7VvHqxD4BHdp/Gd9GVZUkk6lTfVqyt5yHv17GpaNOwhQXRa3XQ1FqKkZFoc7rpdzpJM+RRGFKCkUpqVS5XWyqr+OGiZNQdDpe2bCejlYtVLpcKDpBmsWqie8wHPOienHdWj7asZ0Gn48Gn4/mgP+w4jAqCilmMylmM0kmM7l2B8PSM3CYTCSZTDiMJmxGI3ajEZvBiN1owGowYjMasOgNWA0GLAYDBl1iFx8mgtMKCjmtoJAb3n2b+SNHAWBSlFaRKEKQarHgDMaWWziDAexGU9wifntrrevgd9218FMWl8fi3jmMJtKtFjKtNjKsVjJtNjKtNrJsNrLt9tjWZifFbD7q/l69yTEvKlcwiC8cpiA5mfG5uWRYraRZLKRZrKSaLaRbLaSYLaSazVgMx+bixI5YUVXJh9u3E4pGmZKXz22ffMSfZ5/NNWPH89tFX6BKyfyRoxiYmoonFOKhZaU0+Hz0T0ri0pGj+ONXXwIwZ/AQDB1YnxsmTeasQYNp8vtp9PtojF/MtjY28FV5Oe7QoauuTYpCtt1Ort1Bjt1OrsNBP0cS/RwO+jkc5DmScHTSIh8LaIsUjxNiS+0lOiEIRiKtF5Bmv5+olKRbLAghaPT58EfCGHSxEz2qqmxuqCeiqozKzOpQVB0RiISp83pbU43HQ63HTbXHQ43HQ7XbTa3XQ0Q9MN5GsslEflIyeUlJ9E9Kpn9yEgXJKRQkp5CflHTUDTW1RYonALGl9rEh1v4WOdVy4FsJ063WAz4rOh0nZWUnrB9mvaFVDIcjqqo0+HxUuV1Uut1UulxUul1UuFyUNTexaPcugtFvpwLphCDPkcSAlJR4SqUoNZWBqankOZIOGL4eDWii0uhzFJ2ObLudbLud8bmHHpdSUu+LOVbKnU72tDSzq6WF3S0trN6yGU8o1JrXqCgUpaQyKC2NQampDE5LZ3BaOgNTUzHpj8zpnZBWhRBPA+cBdVLKk9o4LoCHgLmAD/iulHLVwfk0NCBmdbNsdrJsdib1O/BxgpSSBp+PXS3N7GpuZmdzE2XNzWysq+OjHdtbnVQ6IShMTmFoejrDMjIYlp7BiMxMCpJTOnTG9JRESfkZ4BHgucMcnwMMiaepwGPxrYZGlxBCxLyMNhtT8g58LU4wEmFXSzPbGxvZ0dTI1sZGtjY28MnOHa0L7q0GA0PT0xmRkcmIzCxGZWYyLCMTq8FAaWkpJSUlzJgxg+Li4m73MSGiklJ+KYQY0E6WecBzMuYVWSaESBFC5EopqxPRvoYGgEmvZ3hGJsMzDlwF7A+H2RYX2JaGerY01PP+9m28vGE9ELNqaQ2NrLn/T0SjUQwmEx9+8gkzp03rVj/6atCZB+zd73NF/LtDRCWEuB64HqCgoKBPOqdxfGMxGBibk8PYnJzW76SUVLndbKqvY2N9HS89+hjRSAQVCIaCzP+/PzJ5Txljs3MYm5PL+JxchqSno++EU6SvRNXWILZNX76U8kngSYi51HuzUxonLkII8pKSyEtKYvagwUyVglkvvEgI0BtNXHX+PFx2Bwt3lfH6po0AWPR6xmTnMC6nDe/KfvSVqCqA/dct5wNVfdS2hkaHFBcVsVBKSubOZcYvf9l6TyWlZK/LyerqatbUVLOmpoanV69st66+EtU7wI+EEK8Qc1A4tfspjaOKlSspBopvvx32c1IIIVqfu80bPgKIOUTMP/7ZYatKlEv9ZWAGkCGEqAB+TTzYt5TyceADYu70HcRc6t9LRLsaGglj5UoQAsaP7zBrR8+/EuX9u7yD4xK4ORFtaWj0CitXwtCh4Oj5erKja36HhsaRYuVKmDgxIVVpotLQqKmBykqY1Ob82C6jiUpDY2Xcm5cgS6VNqO1lpJREovFl9dHY0npVjb33t83l9MSW0QshUJTYamFF0aFXdEfdbOzjhi44KTqDJqo4qirxBkO4vAFcvgBuXxC3P4jHH8IbCOILhPEEgviDYXzx5A+GCYTCBEIRguFYCoUjBMNRwtEo4UiUqJq459dCgFGvYFAUjAY9RoOCSa/HZNRjMugxG/VYjAasJgMWswGryYjVZMBuMWEzG7FbjNgtJhwWE0lWM0lWEw6rGb1ygos1gU4KOI5FJaXE7QvS4PLS4PTS5PbR6PLR5PbR7PbT7PHR4vHj9AZo8fhx+YIdxqgwGZTWE9ViNmI26DEbDWQkmzDHT+x9J7pBr2DQK+jjVkavi211OoFOt++l2sSUsn+/1ZgFU9XYosOYdVOJRFXCkVgwmVA4JthgJEIwLuhAKEIgFMblDcQEHwrjC4TwBdt/dy+A3Wwk2WYm2W4hxWYh1WEh1W4hzWElLclKusNKerKN9CQrqXbr8SfClSth+vSEVXfMi2pdWTUbd9dQ0+ymrsVDbbObBqeXeqeHYPjQmNd6nY6U+EmTYrcwJD+TFJuZZJul9cqdZI1dyfdd2W1mIzaLscerYo8Eqirxh8J4/MF4CuH2B3H5AnGrHMTp3XdxCdDi9bOrpolmj49AKHJIfTohSEuykpVib005qQ6yUx3kpDnITUsiI9l27AgvwU4KOA5E9eHyLbxasgajXiEr1U52ioPRRblkJNvITLaREU9pDivpSTaSrMf+i5q7gk4nYhcFs5Hs1K4Nb/zBMI0uL01uf6vF33fBqmvxUFHfwoptFXj8B8alUHSCrBQHz/5iARnJtkT+nMSTYCcFHAei+uGcqVw/dyopdssJJZa+wGIykJ+ZQn7m4ZfGA3gDIWqb3dQ0u6lpclPV6KK6yUWy3dxuuboWD28t2cDWvXWcMX4IZ00a2joaWLmtgqpGJ5OHFZCT5sAbCBEKRzCbDFiMCQzgk2AnBRwHokpLsnacSaNXsZmNDMxNZ2Bu268QPRxZKXaunDUBKSVPf/QNOyrTGFGQzRdrdlDV6CIQilCybieXTBvNh99sZmd1E8FQhGtmT6R/VgrPf7qSTeW1fGfGOCYOye+4wbZIsJMCtOdUGkcQKSU2s5HPVm8nPzOF7JTYib10026KRxZy3ZwpVDY4WbW9Ek8gxC3zTmVkYRbBcIR/f7ScYf2z+PmlM1i1PWbVukUCZ1LsQxOVxhFDCMFri9ZiNuiZd8qo1lFHKBzFbonFAQyGIkRVFbNBj17RYTUbCYQjlNc10z8zmcwUO3UtHiJRtb2m2qYXnBRwHAz/NI5dPl25jf9+tZ7h/bMQCDbvreXmC05l+thBlKzdSYrdTE6agxEF2Xy9uRynN8Cu6ibGDuyHxWTAZIydvpGoit3cjWCcveCkAE1UGkeQMycMoXhkIcFwBFVK+mUkoVd0TBtdxCcrtlHX4uXCU04i1W6hf1YKr5SsiYU3S3WwYOZ4/vn+10RVlRljB5Fit3TY3ntfb2JIvwwG52XEZqf0gpMCtAi1GscwTm8AXzBEVoq9wylcLm+AGbc9BsQedo8Z2I+fv/Qg2XVV6LZswWjomn3RItRqHJck28wk29p32+/DYTXx3r3XsWZnJWt2VLF6RyXm9ev4PHcQv7/1UUYX9WPysHwmDe3PSUU5PXrQr1kqjROTmhrIzWX7rXfx9tTZrNxWwbbKeqQEq8nAhCH5nDyigJNHFFKUk3bIM1DNUmloHEzcSTHkgrO57fTTgdhwcsW2vXyzpZxlm8v5asMuALJT7RSPGMApowqZOrwAh7V966iJSuPEpA0nRbLNzKzxQ5g1fggAVY1OSjftYdnmPXy2ejtvLd2AohOMHdSv3ao1UWmcmHRiJkW/9GQumTaGS6aNIRJV2bC7miUbdrM4bsEOh3ZPpXFikp8PM2bACy90q3h791TajAqNE499MykS/NB3H5qoNE48emkmxT40UWmcePTSTIp9aKLSOPHoheUe+6OJSuPEY+XKhM9M3x9NVBonFr3spABNVBonGr3spABNVF3iaH6mp9FJetlJASfwjIpQMBZ+y2j69k8QDIbZvbMeo0lP0aAsIpEomzdU4vUGychwMHhYDjXVLXz6wTrSMx2cPXcsir7965KzxUddrZNwOEo0ohKJRGMx/aIqUpUHvE5SAAiBogh0ii4WmVavQ69XMBr1GAwKRpMes9mAyWzAaNRrwW66Si87KeAEFdXWTVW8/NwS0tLt/PjncwCIRKIs+2o7q1fsIinZis8XJDsnhU8+XMfQ4blsXL+XvII0Fn+xmYKiDMKhKB+8u5rzL2p/GPHFpxv5x4Mf98rvEALMFiMWixGL1YjNZsJmN2Gzm7E7zCQlWXAkWUhOsZCcbCUl1UZKqpXUNDsWq7FX+nTUs3JlbCZFL3JCimrYyH787I5zeeLhT1u/c7b4WL5sJ7fdfT7OFh9PPvIZF39nKoMGZ3P+RRN5/aVSdm6rYVdZPZdeUYyzxccTj3zWoaimFA8iM+tSDEYFvV6HoldQWiPVCgQiZqLiJisWnVYlGonFXo/ErVs4FCUUisRSMEIgECYQCBHwhfH7Q/i8Qby+IF5PkKbGBtzuAG6Xn3Do0ICiAGaLgbQ0O+mZDtIz7GRmJZGRmURmdhJZ2UlkZSeTkmo9vixhHzgp4AQVFYDQCdT94pzr9QrhcGxIaDAoRCJRolEVofv2pFL0Cmo8wIjRpIdO3GP1y0+jX35agnvfeQKBMK4WH83NXpwtPpqbvLQ0e2lu9NLY4Kax0cO2zdUs/XIboYMi0ppMerJzU8jtl0Juv1Ry81LJy0+lX34auXkp6PXHWMTePnBSwHEgqk3rK1i3ppzy3fWU725kSvEgrvlBx3Gx1ahKIBAmEonidvmx2c1k5SSzdVMVLpefYSP6kZ2TzAfvrGbZku3U1bgYdEk2Y8YX8vJzS4hGVabPGtUHv7BnmM0GzDnJZOUkt5tPSonL6ae+1kVdrZPaGie11U5qqluorm5h3Zpy/L5Qa35F0dEvP5WCwgwKBmQwYGAmhUWZ9C9Mx2g8Sk+rPnBSwHEgqs8/3cDb/1lBRqaDggEZpGd0fAPa3OTl6cc/p67WxZuvLaemuoVbbj2H8y+ayJuvLcdqNXLJgqlYbSYmThmI2+Xn1OnDMJr0zJw9ijUrd2M2GxgzvrAPfmHfIIQgOcVKcoqVwcNyDjkupaSl2UdVZROVe5vYW97I3j2NlO9uoHTJNtRozGrrFEH/gnSKBmUxaHA2g4bmMHhoNqlp9r7+SYfSB04KOA6WfjQ3eTEaFWwdhBjW6D3C4SgV5Y3sLqtn1846dpXVUba9lrpaV2uetAw7Q4flMnRELsNH5jF8ZD8cSR1HQEooPVzusT/H9XL61LSjPAD+CYDBoFA0KIuiQVnMnP3tkNjt8lO2o5Yd22rZvrWabVuq+Xrp9tZb0f6F6Ywanc/I0fmcNKaA/IJDY0EkjD5yUsBxICqNoxdHkoWxEwYwdsKA1u+83iBbN1exeUMlmzdUsOTLbXz03loAklOsnDS2P2PGFTBmXCEDh2Sj0yVIZH3kpABNVBp9jM1mYsKkIiZMKgJi92p79zSyYd1eNqwtZ/3avSxZtBWApGQL4yYOYOLkIiZOGUh2bvtvH2mXPnJSgCYqjSOMEIKCATEP4twLYid8Xa2TdavLWbViF6uX7+LLzzcDkF+QxqSpg5h88iDGTijEZOrCK3X6yEkBCXJUCCHOAR4CFOBfUso/HnR8BvA2sC9ixn+llL/rqF4tRoWGlJLyPcbJqBAAACAASURBVI2s/LqMFd/sZO3KPYRCEUwmPeMnFVF82hCKpw3t2LuYQCcF9LKjQgihAP8AZgMVwHIhxDtSyk0HZV0spTyvp+1pnFgIISgckEHhgAwu/s4UgsEw61aX883SHSxbso1lS7bzt//7gJGj85k2YwTTZgw/5Jlc6XvvUVJZyYz0dIr7os89tVRCiGLgN1LKs+Of7wSQUt6/X54ZwG1dFZVmqTTaQ0rJrp11LFm0la8WbaFsRx0Aw0f24/QzRjL9jBHs3LWJWTNmEAqFMJpMLPziC4qLey6t3nap5wF79/tcAUxtI1+xEGItUEVMYBvbqkwIcT1wPUBBQUECuqdxvCKEYODgbAYOzubq606nsqKJxV9s4csvNvPkI5/x5COf4VfXEgyFUIFQJEJJSUlCRNUeiRBVWz7Pg83fKqBQSukRQswF3gKGtFWZlPJJ4EmIWaoE9E/jBCEvP40FV5/CgqtPoaqiiS8+3cjLLzRjBMKATihkZw4mGlVRlN5bSpiImiuA/vt9zidmjVqRUrqklJ74/geAQQiRkYC2NTTapF9+Gld+bxrv3nM+nwNXj51G8YQf8vLTW7n6kod5/qkvaah3dVhPd0iEpVoODBFCFAGVwALgiv0zCCFygFoppRRCTCEm5sYEtK2h0S7ixRcpttkoXvIhIYOJ0q+28dG7a3j+6S954ZnFnDJtGBdcPJFxEwckbDZHj0UlpYwIIX4EfEzMpf60lHKjEOLG+PHHgfnATUKICOAHFsijedJhLyKl/HYFcFSNTdnZ96doXfWroDfo0HXwIjONDggE4PXX4eKLwWbDCEw/YyTTzxhJdWUz77+9mg/fXc1XJVsoLMpg3iWTOXPOaCyWni3gPOYn1PY1oWCE5noXLQ1uWho8OJs8uJq8uFu8eJx+PE4fXncAnyeA3xMk4AsRDIQI+EOEQxEih1k02BaKXofBqMdoNmC2GDFZDFhsZiw2E7YkC/ZkC/YkC/YUK8mpNpLS7KSk20nJsJOalYzVbjq+Fhl2lTfegPnz4eOP4ayz2swSCkZY9Pkm3nx9Odu3VONIsjBv/iTmXTKJlNTDzyttz/uniWo/pJQ017upKW+kZm8jdZXN1FU0UV/dQkN1C401TtwtvjbL6g0KjhQrtiQLNoc5dvLbTVisJkwWA0azAaPJgMGoR2+Mr/6NrwAWQiClRMrYOq9oVCUajhIORQiHIgQDYYL+EAFfiIAviM8dxOcJ4HH5cbf4CPpDbfbJZDGSkZNMek4ymbkpZOalkpWXRk7/NLL7p5OVl4recIwtNOwKF14IX38Ne/eCvv1BmZSSjesreP3FUpYu3obJpOec88dx6eUntzk9ShPVQUQjUSrK6infVkP5jhrKt9dSUVZH1a56Ar4DT9DkdDuZuSlk5KaQnpNMenYyaVlJpGQ4SMl0kJJmw5Fqw2I7clYhFAjjbvHhavbS0uCmud5NU72L5joXDTVOGmuc1Fc101DjbF25DKBTdOT0TyNvYBYFQ7LpPzibwqE5FA7NxWLrxtvejyYaGyE3F265BR54oEtF9+xu4PUXS/nso/UAzJ47hqu+e9oB4jqhReX3Btm5oYIdGyoo21TJzk2VlG+vaR2GCSHIzk8jf3AWeUWZ9BuQSU5BOjn908jKT8Pcw/H10UQ0EqWhxkltRRM15Y1U72mgsqyeirI6KsrqCAe/XU6f0z+dgaPyGDiyH4NG5TNkdH/SO1g9fFTx+ONw002walW3J9HW1Tp5/cVlvP/2KqSUzLlgPFd+9zTSMxwnjqhUVWXP1ho2rihj6+o9bF1TTsXOutZ4fSkZdgaOzGPgiDwKh+UwYFgu+YOzjyvhdJdoVKWmvJE926rZs7WGXZurKNtcSdWuhta/X2pmEsPGFTB0XAEjJxYxbHzh0fu3O+00aG6GDRtis9N7QF2tk5eeXcJH765Br9dx4aVT+OHNs45fUe3ZWs3KL7ewrnQHG5fvwuOM3fMkp9sZNraAoWMLGDy6P0NG55OWfQxdaY8S/N4gOzdWsmP9Xrav28u2dbELFcTuI4eM6c+YkwczungwoyYVYbYeBcPGsjIYNAjuuw/uvDNh1VZVNPHcv77k80838OnSe45fUT30i1f46JVl5BVlMnrqIEZNGcioyQPJKUg/sT1fvYi7xcfmlbvY8E0ZG77Zyba15UQjKnqDwoiJAxh/2jAmTB/O4JPye3XmwmG591645x7YvRsKEx9HZMfWGoYMzz1+RVW7txHFoJCR04MFbBo9wu8NsmlFGWuWbGfNV9vYubESKSVJaTYmzxxJ8VknMXH68L6xYlLCiBGQkwMlJb3WzHEdoyK7f/qR7sIJj8VmYuL0EUycPgKAlkYPqxdvZcUXm/n6s40sfGM5RpOBiTOGc9qcsUw9cxS23gr6smIFbN0Kt93WO/V3gmNeVBpHHynpdmZeOJGZF04kEo6ycXkZSz9ax5KP1lH68Xr0RoVJ00cwfd4ETjlrNEZzF1bwdsQLL4DRGHvoe4Q45od/GscOqqqydfUeFr+/hi/fW0NjjRN7koXTLxjP2d85mSFj+vfsPjgchrw8OP10+M9/EtfxNjhhXOoaxw6qqrJ26Q4+e/0blny4lmAgzMBRecy5vJiZF03C5uhGHMcPP4S5c+HNN2OzKXoRTVQaRzVel58v3l7JRy8vY+eGCsxWI2ddNpULr5tObmEXVghdeWVMWNXVYOpdp4gmKo1jhq1ry3n3mcUsemcValTl1DljueTGMxg2toNV4G43ZGfDtdfCY4/1ej81UWkcczTWOHnnmS95/4UleF0Bxp06lCt+ejajpw5qu8Dzz8M118BXX8Gpp/Z6/zRRaRyz+DwBPnhxKf99soTmehcTpw/nu784l8Gj+x+Y8ayzYPv22GyKPnjo356otFVwGkc1VruZ+Tecwb+X/JLr7r6AbWvLueXcB7j/5mep2t0Qy1RVBQsXwlVX9YmgOkJ7TqVxTGAyG5l/wxnMubyY/zzxOW/+s4SlH69j/g1ncIW6EYOqxhwVRwHa8E/jmKShpoV/3/8eb7zyLqc3f8g5uZmcsWdnn7WvDf80jjsyclI4bcEg1ra8xV/Dbs4p381Nl9yDq9l7pLumiUrj2KXkiy8Ih0JEgaiAki9KuGn2n1j15dYj2i9NVBrHLDM8HoyAotNhMpv43cO3YUuycPdVj/HPe98mfNCLwfsK7Z5K49ikqgpGjqS0qIiSSy9lxsyZFBcXEwyE+Ne97/Dec18xcmIRdz/xPdKykhLevPacSuP4QspYLL+PPoK1a2PvnTqIL99dzV9ve5mkVCu/fuoHDBqVn9AuHNfrqY5WfG4/deWNNFY301zTQkuDC3eTF0+LF78nQNAXJBQIo6oqalRF6HQoig69QU9OUSY3/N9VHbaxadk2Pn52ESNPHsLJ504gOSOJSDiCs8GN2WbClmTtg196BHjjDXjrLfjTn9oUFMDp548nb2Amv/n+v7j14r9z16PXMmXWqDbzJhrNUvUAVVWpLqtj98a97N5Ywd6tVVRur6ZqZy3uNrxQOp3AlmLD6jBjspgwmPQoegWdokOqsXh/kVCUzP5p/OGd29ttu7nWyZK3l1N0Un+2rigjuzCDU+dNxtXk4e1/fMyeTRV85xcXMGR8Ebs27GX15xuwp9gYN2MkWQUZeFq8RCNRkjMSPzTqVZqaYit78/NjMf06iOfXVOvkN9//F2WbK7n94WuYdu64hHRDs1QJwtXoZv1XW9hUup1tK8vYvnoXPpe/9XhWQQb5Q3OZflkx2QUZZBVkkJGXRlp2MsmZSViTLAkL5Vxf2YjZZmbUKcPYsnwn0Ugsnl9Smp15N5/N4v9+jaLEAmWuKdmINclC3d4Gdm+qQG/U89kLi1n/1RamnjuBOd+feWRiSXSH//3fmLA++aRDQQGkZSdz/ys386trnuCPP3qOSDjKzAt792XamqjaQUrJrvV7KX1vJd98uJot3+xESonBqGfg2EJmXXEag8cPYODoAgpG5GGxdWMNUHf7pspWITRVtzD57LGtx7wtXiKhCI40G811TqLhKKdcMImty3diMOl58+GPGDdzFJfddj6v/N87bF62jZNOHd5nfe82n3wCzz4Ld98NY8d2nD+OzWHm3hdu5FfffZK//PQFrHYzU8/svaGgJqqDkFJStnYPX7xayldvfUPVzloAhk0ayJV3X8TEM0czZOJAjF15iXMvMGzSID5/ZSnb1+zCkWpn2furyCnKQghB5c5a/J4gZpsJo9mI1+kjKc2Oq9FNv0HZtNS7SIsHymmuc2K29t3FoNt4PHD99TB8OPzyl10ubrGZ+N0z13P7dx7h/puf5c+v38KQMf07LtgNNFHF8XsDfPrcl7z7+Kfs2VyJolcYN3Mkl956HsXnTWw9CY8mrrzzQhqrW0jOcLDqs/UIIagrb2Dp28sp31JFWk4yZ10znXAwwpsPf8juTRVMmDWagWMKcDd78HsDqJEoqcdC5Nm774bycli8GMzduwhYbCZ+8/QP+dmFD/Lr7/2Th9+/tVei7p7wjgpXo5s3H/6Idx7/FHeTh2GTB3H2tdM5/ZKpJKU7ul1vNBKluqyWqp211Oyuo668kebaFlrqXHicXnwuPwFvkGg4SjQSRegEeoMeo8WALcmK1WEhOTOJ1OxkMvLSyC7MJHdgFvnD+nV6mCmlRAhBQ2UTteUNRCNRxkwbgafFywt/+C+uRg8X3XIOQ8YXdft39jalpaWUPPssM554guJbboG//73Hde7ZWs1PLniQ4eML+cOLN3XrflJ7TtUGrkY3r/3lPd55/BMC3iDF50/kslvPY2Tx0C4HH1FVle2rdrFx6Va2ryxj59o9VGytOuCJvt6gkJKVTGp2MvZUG1aHBbPNjN6goOgVVDX2po+gP4TfHcDj9OKsd9Fc68TvCRzQXnZhJkWjCxg6sYhhkwczZvrIoyMybIIpLS1l1qxZhPx+jEKw8NNPKZ41KyF1f/zqMv7281f43u3ncdnNZ3a5vOb92w8pJYteX8Y/fvYsrgY3My4r5vI7LmRAFx8OhgIhVny8lq/eWs7yj9bQUucEIC03lcHjBjD5nHEUDM8jb0gOOUVZpOWkdNvz52nxUrOrjqqdtezdWsnujRWUrdvD1+/HAucbTAbGTh9J8QUTOe2iqUflULU7lHzwASG/nygQEoKSb75JmKjOumwqK77YzPN//ZBT544lrygzIfXCCWapmmpaeOjmpyh9dyVDJw7kZ4//kEFjOx8WWFVV1i3axMfPlLD07RX43H4cqTYmnzOOKXPGM3bmKDL6pSWsvx3h9wTYVLqN5R+t4esPVlGxrRohBGOmj2D21dM5ff7JWOzHgBOiLXbsoPSMM5i1dy8hnQ6jycTChQsT+mb5plonP5h5H6OnDua3//5hl8pqwz9g3eLN/O6yBwl4g3z3t5dx0S3noOg798KzaFTl8xcX8/zv36C6rBZbspVpl0xl+qXFjJs5Cr3hyBt8KSW7N+7ly/8s4/OXl1C1owaL3cz5N85mwR0X4ki1H+kudp4lS2DePABK772XkuZmZsyYkVBB7eM/T3zOU394hz+8cBMTTh/W6XLtiSr+Br+jM02cOFEmgi/f+FrOtV0tv3/SrXLPpooulV3xyVr5w7G3yTN1l8n/mXKHXPjiYhnwBRPSr95CVVW5fvFmef9Vf5ezle/Ii9K/J1974B0ZCoa7VV84FJaRSDTBvTwML70kpdEo5ZAhUm7f3uvNhYJheeXkX8k7FvyjS+WAFfIw5+0RF057KRGi+vjZRfJs0xXyJ6f/Wjob3Z0u11DVJH9zyV/kmbrL5DVDbpElry6Vqqr2uD99zc61u+Wdc++TZ+ouk98b+VO5pmRjl8pHo1F57xUPyT9c+XcZCUd6qZdSSlWV8ne/i52Sp58uZUND77V1EK8+8qk8p/9PZNmmyk6XOWFFtf6rzfJs85XyF+f8Qfo8/k6XK1u3Ry7of6M813aVfPG+/8pgINSjfrSFqqrS6/LJxuomWVVWI+srGqSryd1rJ+6y91fJa4bcIs8yLJDv//OzLpV99c/vyNmGy+W/7nq5V/q2tKRE3jd+vFwKUl51lZSBQK+0czhczR55/uBb5WO/eqPTZdoT1ZG/GeglXI1u7rvqEXKKMvnVqz/t9LOdjUu38svz/4TJauShJb9n0NgBCenL+sWb2bZiJzvW7KJ6Zy115Q1tvgBbp+han0sVjS5gyMRBjDplKPlD+/UozvjUueMZPW049y74Gw/e8CSuRjff+cW8TtV52W3nU1VWy6t/focxp484YEpUj/D5KL37bmY99BAhKTHq9Sy86SaKezm67ME4UmxMmDaM0k/Wc8NvLurxe82OW1E9ftvztNQ5+ftXv+/0EoiydXu4/ax7ychP548f3UXOgKwe9WFT6VZevv/NVte3TtFRODKfASf1Z8rcCaTnpmK2mTCYjUTDEYK+EM4GF3V7G6guq+XT5xbxzqMfA1A4Mp/5t17A7KtP77SD5WCsDgu/e+vn/OX7j/HUXS+jGBQu/d/zO1X2pgeuYVPpdv7yg8d5ZsuDPZvn2NICjz4Kf/sbJfX1hCDmNpeSkkWLKD7llO7X3U1OOWcMX3+2kbJNlT1fe3U4E3Y0pO4O/+r2NsizzVfKx257rtNlotGo/NHJd8n5OT+UTTXN3Wp3Hw1VTfL+qx6SZ4r58uKM78mn7npRrv9qswz4ujasiUQicvemvfLtf3wkrx93qzxTzJfXj71Vrl+8qUf9i0aj8tcX/1nOsVwpK3dUd7rcusWb5WzD5fK9Lg4f97H0vffkfTNmyKVWa+zOY84cufTRR6XFYpGKokiLxSKXLl3arbp7SvWeBnlO/5/I919Y0qn89PY9FXAOsBXYAdzRxnEB/D1+fB0woTP1dldUT9/zqjzLeIWsKqvtdJkP/rVQnqm7TH7y3KJutbmPhS8tlhckXS3nmBbIp+9+qUv3cu2hqqpc9PpSeXnBDfJMMV8+eP3jMhLp/v1XfUWjPD/pGnn3eX/sUh9umnyn/MHYn7frtFm6dKm877775NIvvpDys8+kvOMOuXTECGkBqYC0KIpc+u9/H5r/CAlKythvu2TU7fLvd77aqfztiarHwz8hhAL8A5gNVADLhRDvSCk37ZdtDjAknqYCj8W3vcLX769i3MyR5BZ1fvj2wVMLGTKhiDOvmtbtdp0NLv76g8coGl3A7c//mPwhud2u62CEEJw+v5jJc8bz9J0v8dYjHzJmxijOuPy0btWXkZfGpbeex3O//Q9NNS2dmoWxbNkyPLk1bHm/gprd9eQWZcXm5pWUMGPCBIpTUyl9/31m3XcfoUgEI7AQKNbrKcnLIyQEUSkJASXV1ex76lRcXNwrz6C6ghCCgiE5VO1q6HFdibinmgLskFKWAQghXgHmAfuLah7wXFzhy4QQKUKIXClldQLaPwApJZU7axk7s/PrZSLhCDvX7GHezWf36Cb1nUc/JugPcdvT/9MlQZWWxl5PO2MGdHRuWWxmbvrbd1n56Vr+88A7zFxwarf7PG7mSTz32/+wfWUZU8+dcGi/nnqKktJSZgwdCn4/s/7wB0KRCIqENQvms1sfZdayZYRUtVVAJfDtPZIQlFxzDcUPP8yMDRswzppFKBTCaDQyY8aMbvW5N3EkW2mqc/W4nkSIKg/Yu9/nCg61Qm3lyQMSLqqWOhdBX7BLVkqn6Pj70nuxdudFY/vxybMljJs5isKRnV+nU1oKs2ZBKBR7q+bChR0LS6fTcf5NZ/PoT//NrvXlDBzTvTewD4xP0Spbv+cQUZWWljLrBz8gBBiBa/lWLADL163CkJpESFW/FdBVVzFjzhyM1133rXhuuAEcDoqLi1m4cGHMqvXS7IieYnWY2buzrsf1JEJUbV0mD5771Jk8sYxCXA9cD1BQ0ME7idrAlmxBCIG7ydPpMjqdjsHjBnS5rYMpGl3AxiVbCfiCnZ41XlISE1Q0GtuWlHQsKoDNX2/D6rCQ3ZWXoh1EU3ULAKlZhw79SkpKCOl0RFWVkKLA/PkY336bUCiMVCHjlw8y/oyTDrQ+N90UE8+AAW2K52gY5rVHOBTBaOq5JBIRmKAC2P/SnA9UdSMPAFLKJ6WUk6SUkzIzuz5z2Gg2kpGfRuWOmi6X7SmX3noBrkY3b/39g06XmTEjZqEUJbbtzKho1/o9LHqtlLk/PBNbsq3b/d2+sgyAoZMGttGvGRhNJhRFwWg0cs1PfsLCzz/nusuvZ6JyBmfNnd1qfX7/+98fMNm1uLiYO++886gWUFt4nH7syT2PQJUIS7UcGCKEKAIqgQXAFQfleQf4Ufx+ayrg7I37qX0MGV/E6s83EAqG+3TZ+0mnDWfiWWN56q6X2LpiJzf99VqyCtq/MBQXx4Z8nbmnCgVCvPbnd3j5/v9iS7Zy8U/P7XZfVVXlzUc+JDU7mYIReW30q+3h2tKn11Fl95M/LLc137EmnsNRX9XMwJGH/i26zOHcgl1JwFxgG7ATuDv+3Y3AjfJbl/o/4sfXA5M6U293XerLP1krZxsul5++sLhb5XtCKBiSL933X3mu9Qp5rvUK+a87X5SN1U09qjMYCMmP/v25vGbwzfJMMV/+/jsPyLq9PZsb9/4/P4s9Qni2pNNlmuuccq79GvnQj57qUdtHI163X57T/yfypYc+7lR+enuakpTyA+CDg757fL99CdyciLY6w8QzR9N/WD9e+dPbnH7JFIxmY181jcFo4PI7L2LWlafxz9tf4NU/vcVr//cWA0YXMOqU4QydOJD8oblkFWSQlpt6wLIRVVVxN3moK4/NqNixehfbV5WxcclW/J4AA8cW8qdP7mHCmWN61Me1izbxxG3PM/r0EZx59emdLvfqn98hHAwz76azetT+0ciO9TE/2qBRPbdUx+U0JSEEN/7lau4+/088efuL/Oih7/V5H7IKMrn75Z9x7W+/w8IXF7OpdCsLX/iSdx/7+IB8eoOCyWoiEoocMhdQ0SsUjspn1pXTOPWiqUycPabH89KWvr2cey9/iNyBWdz5/C2drm/FJ2t5428fcN71sygcmdgQykcDyz7dgMGk56TDvVO4CxyXogKYfPZYLvnpXN742wcMnzKEM6/s3kPSnpI/tB/X/vY7QMwSVe2spbqslro99TTVtBDyhwj4ghhNBkxWE/YUG1mFGeQMyKJgRF7CrGwkHOH1B97lmXteZeikQfzhvTs6HdimuqyWP333UQpH5nN9J8JRH2tIKVn68XrGnzoUawJWSh+3ogK47g8L2L5qF3+57jGikQhnXzvjiPZHp9ORPyQ3oTMtOkJKyYpP1vLEbc+zZ1MF0y6Zys+f/p9OL7Pfs6mCO+bejxpVueeVnxyXAWZWLd5K7d4mrv7fOQmp77gWld6g5/dv/5zfXvogD/zwSZpqnCz4xQXdGkJt+GoLnzy3iJEnD+WUeZNar/Jep49wKEJK5tEXk3zrip08dddLrF64gZyiLH731i8oPr/zIY83Lt3Kry5+AL1B4S+f3UPB8AR4xo5C3vpXCamZDqadNz4h9R3XooLYtJ7fvXkbD/zgCf59z6tsXb6Tn/zjOlKzOx9EsammhV0b9nLO92eyedl21i/ewqkXTqZqZw3L3lvJ6oUbGDtzFPN/dh6LXi9lzRcbmTp3PAPHFpLVPwNng4ugP0R6v7Rej1neUu9i0eulfPxMCdtXlpGU7uCmB6/lvBtmd/rxQjQS5fW/vs9zv32d7MJM7nvvdnIHZvdqv48UW9eWs6JkC1ffOichD37hBBAVgNFk4PZn/4chE4r49z2v8oOxP+fGP1/FmVdN65TVqt/bgNVhZuTJQ9m4dCuRcCye3xevLqVwRD6/f+d2XvvLO+xaX075lko+e/5L0nJTGHHyEKrLaln0n2VsWbadibPHMOcHZyQ8UEztnnq++WA1i9/8mrVfbERVJYPGDeCmB6/l7GtnYOvCA82da3bz1xv/yfZVu5h28RR+8o/rehRU9GhGVVUe//UbpGY6mPf96Qmr94QQFcTuZ+b/7FymnDOOv974T/583eN89tJXfPe3lzFiyuAOy4t4zL7mGidT5sSGCS11LsbNiFk8V6MHn9vPxT+ey6nzJrPkrW8QOh2fv/wVwyYPZsEv5vHS/W+yedl2Rk8b0e3f4XP7Kd9cyc41u9m+qowNS7ayZ1MFAHlDcllwx4VMv7S4y/MBm2paeO2Bd3nrkY9JSrfzy5d+zLRLpvbY23g0s/CN5WxZtYf/feAKbD2c97k/J4yo9lEwIo+/fvEr3nviM5797X/4yWm/YuLs0Sz4xTzGnD6izZNo2OTBfP7yEravKiM5w0HpuyspHJFP/2G5BLxBAr4gkVCEtJwUbMlWBo4p5KX73sTn8uF1+luHmi11TqxJlg77uGrhetyNHprrWv6/vTcPj+M48zTfyKysrLsKhRsESJAURYqUKFGiqFvWZV2jWy21R/LaveNuzbgP93h33fas3fPMeMZHz/RuH273rj1yj221ZXe3ZdlqHW5d1mnJpERRpCiS4gESAHGjqlB3VR4xf2QBJCWCBAiQBMB4nyeeyKqKyoysyl98kZHxfUF6cIzh3hQD+4cY2DfEcO/oRLlIIszKi5dz87+5lg23rKNj5fRd7gcPDPPTv3yaZ773InbV5sZPf4zf/cYDxJLzKKTZCTDYM8r//58eZ83Fy7j+3qNHGjtRzjhRgWe17vjsjdzwyat48jvP809/8RRf+Ph/5eyLlnHvH9/KFXet/8hQ9oNfvof04Bix+gjvvOBNgbrx09fw9//lMZ774cvc9Ue3oBs63/vyjzH8PiKJEImmOK3LmskMZckMZ5GSKfkt/dmn/obUQKZWV0GytY6WpU2cf81qOlYtYsk57Sw9r4PWZc0nZEmklOzcuIfHv/VLXnnsNwghuOGTV/GJP7mDRWe1THt/8w3bcvizzz0CbXD5AQAAIABJREFUwBf+8sFZWzNsnDMmmOaxqJSqPPf3r/LYXzzFwT0DhGJBrrp7A1fdewnrrjsXwz+1tsdxXAa6hkgPZojWRViyup1CtsijX3+c7EiOuz93y5S6Zbs378MwDeKNMWL10VkZ3JBSsm9rN689vpFf/cOv6ds7SCga5Nbfu467/uBmmjrqZ3yM+YCUkm9/5ac89cjrfOlvPsXH7vioH9lUUBFqp4jrurzz4nZe/PHrvP7zTRRzJcLxEBtuuYBLblnH+pvOn1fdIqtq897ru9j4zDu88eTb9O0ZRAjBBdeu5tpPXMFV92xYuOsCT8J4RNr7Pns9/+Y/TC3ozdFQojoBquUqm194j9ce38hvntnC2HAWTRMsv6CTc69YyaqLz+Lsi5bSurx51rsPJ0p6aIzdm7v44K19bH9jF9t//QHlQgXD7+P8a1ZzxV0Xc/nt66f1OGEh8cJjm/jzz/+Iq2+7gC/+zadm9L8pUc0Q13XZ9dY+Nv1yC1tf2cGuTXsn5umFYkE613TQuaadxasW0b6ihbblLTQtrj8pE3kdxyXVn6Z/3xAH9wzQs6uP/e/3sv+9HkYOpgBv7mPnmnbOvXIV6z++lguuW3NKl06di/zLP7zJX/3JP7D2srP46vcfwh+YmUuQWkpnhmiaxjkbzpoYerctmwPvH+SDzfvYu2U/+7f38urPNn7E27iuOU59Wx3JlgSJxhiRujCRhLc2lRny4zcNNF2rrU4vcR0Xqxb/r1yoUMgUyKbzZEfypAczjA5kGOlN4djOxDEM02DJOYu44JrVLFu7hBUXLuWsdZ1nXLfuWDz5w9f49ld+yoVXr+RP/8dnZiyo46FEdQL4DB/Lz19yxDI8Ukqyozl6dw/Qt2eAwe4RhrpHSA1kSA1k2Letm3y6QLlQmfJxDL+PSF2YWDJCsjXB6ktX0NTRQPOSBlqWNtG+opXGjvr5s7L8KcZxXP7nN/+Zx77zKzZcv4Yv/3+/c9IFBUpUs4YQgnhDjHhDjDWXnT1pOduyvWdbhQrVsoXruLiOi9AEmq5h+H0EwiZmyMQfMBb0w9eTSSFX5r997hE2vrCd2z99JQ/9x7vxGScW2Xe6KFGdYnyGj0jCRyRx4rElFMema0cf3/iD73Owa4Tf/y/3cvunTzyW44mgRKVYMLiuyz9//1W+941/JhIL8Y1HP8vay1ac8nooUSkWBCMDGf7yCz/h7Zd3suG61Xz+/3mARP3peaaoRKWY1ziOy5M/fI0f/PencG2XP/jab/GvPnniUXtnAyUqxbxl17vdfPv//id2b+vhwqtX8gf/9T7aOk88uOhsoUSlmHcM92d45M+f5vmfbiLREOWLf/MpPnb7ujkzUqpEpZg3ZNMF/vFvn+eJ77+KlJJ7HrqGf/25m2bVF2o2UKJSzHlymSJP/M9X+NnDL1EuVLjunvV88vM30zxHZ9YrUSnmLMN9aX7+vZd55tE3KBUqXH7zWj71f97CkpWnLhrViaBEpZhz7NnWw+MPv8zL/7wZKeHq29dx/2evZ+k5bae7alNCiUoxJyiXqrz21Bae+dEbvP92F4GQn9s/fRV3feZjNLcnT3f1poUSlWJO8Cf3fYvdW3tYtLSR3/vTO7nx/ktmZVmb04ESlWJO8OC/v5lgxOS8S5bPmaHxE0WJSjEnuOSGqa/RPNdRjjiKGSOlJJcpMNgzSqXseUS/9dIOvve1J3hv477TXLtTj7JUikmxLYfUUBahCeoaovgMne7dA7z7692MDmY579LlXHT1Kn79L9vY/MpOpCu55s4LSTbH6d49wNrLz2L31m6sisW6q1ae7tM5Zcx7Uf38ey+zfdM+zr98BeddspyOFXMnEMt856VfvM1bL+2grbOR8y9fwfmXr2DoYJrfPL8dq2qz8gJvofOxkRzX33MxwbBJ9+4B9u8awG8aXHztagrZEt27B1h31UqklPP+fgngeHFd5r2oqhWLXVsO8NrT7wIQTYRYvX4pqy7sZOX5i1mxtmPejiKdTvJjRcqlKl/4y0/y7q/3TDRcy9e085kv30ExV6Z79yBvPLuNRGOUStmiqb0O23IIhk2GakFo6hpjHOwaPs1nM3vser+Ph//2hWOWmfeiuv/3b+C+z17PQPco723cx3sb97J90z5+8/z2iTKtSxpYcV47y9e0s2zNIpauaiPZHFsQrebJQmgalZKFlBCOB7Gq3qIMdY1R6hq9BQsyo3my6QKLz2rm/bf3Ewz7GenPcNMnLuVXP3+bR//qX5Cu5KrbLvD2OY9/7/37hvnBwy/z2ks7iSeO3Ugv2BBluUyRD7Z2s2drD7u39bDnvV4Ge1ITn0cTIZasbGXximYWr2ihfXkT7UsbaWirU4FU8O6nXnhsEw1tCUzT4LWn3+Wq2y5g1bolPPPoG/QfGKFasfm9P72LUqHM4//jJXSfzorzOrj0xnNJD+fYsbmL1sUN82YmxNHo7R7lkb97hV89t51g0M9vPXAp9/72JYQjARX3D7wuTdfOfrp29LF/Zx8Hdg3QvXuAfLY0UcZn6DS3J2nuSNLcnqRxUR1NbXXUt8RpaE2QbIrNyhKWJxurapMeznlhzQbGGOnPMNibYuhgmsHeFLf9b1dyywOXHXMf6eEcP/jvT9HW2cDq9cvo2TPILQ9cxs539mMG/cTrwiQXaGDOvbsH+ckjr/PKizswDJ277tvA/Q9eSqx2K6GCaR4DKSXp4Ry9ewc52DVC3/5hBntSDPSMMnQwzdho/iPfCYT81DXGSDREiCcjxJJhYokwkXiQcDxIJBYkGA4QigYIBP2YQQMz6Mfw+2pJR9N1dF0gNIEQAiklUoJ0Jbbt4FgOVtXGqtpUyhaVUpVysUqpUKGUr1DIlchnSxSyJbLpAtlUgWy6QGYkT2YkRzZdOGq9mxYlaelI8vH7L+HKW88/qb/tfENKybubD/CPP3qDTW/uJRTyc/s967n3Exuo+1C4byWqGVAuVRnpzzBaa+1TQ1lSQ1kyIznvAh7NkUsXyWYKWBX7lNdP0wSRRIhYXZh4MuIJvT5CsilGsilOfUucxtYE9S1xoonQvL6vOVlUqzavvLiDx/9xIx/s7CdRF+bu+y/mjnvWE5nEV0tFqJ0BgaCf9mVNtC9rOm7ZatkiP1Ykny1RKlYp5cuUi1XKpSqVUtWzPBUbx3ZxbAfHcT0L5coJiyU0gc+no/u0CcvmrVzvJxDyEwyZBCMm4WiQSDxIMGwqoZwgQ4NjPPXzzTz9xBYy6QIdi+v53Bdu4cZb12JOcSnXo6FENYv4AwbJQHzB3mcsBBzHZfOmLp76+WbeeO0DpJRccvkK7vyt9Vx48TI0beYN1IxEJYRIAv8AdAL7gfullOmjlNsP5AAHsCczmwrFyaK3J8VzT7/Lc7/cxvBglkQixH0PXMZtd19IS+vxF+KbDjO1VF8CXpBSflMI8aXa6y9OUvZaKeXIDI+nUEyZbLbEy8+/z/O/3Mb77/WiaYKLLlnGv/3DG7j86pUYJykM9ExFdSdwTW37B8BLTC4qheKkUyhUePO1D3jphfd568292LZL57JGfvf3r+P6m86jofbg+mQyU1E1Syn7AaSU/UKIye7mJfCsEEIC35FSfneyHQohHgIeAli8ePEMq6c4ExjLFHnjtQ947aWdbN7UhWU5NDZFueu+DVx/07ksX3FiayOfKMcVlRDieeBoqyt/eRrHuUJK2VcT3XNCiJ1SyleOVrAmuO+CN6Q+jWMoziD6D6Z547XdvPHqLra+243rSJqaY9xx73quunYV56xpn5VBhxPhuKKSUt4w2WdCiEEhRGvNSrUCQ5Pso6+WDwkhHgc2AEcVlUJxNCoVi63vdPPWb/ay6Y299HSPArBkaQO//eDlXPGxlZy9qnVOPF6YaffvCeDTwDdr+S8+XEAIEQY0KWWutn0j8NUZHlexwHFdyb49g7zzVhdvb+xi25ZuqlUbw69z/rol3Hb3RVxyxVksmoNBYWYqqm8C/yiE+AzQDdwHIIRoAx6WUt4KNAOP11oQH/ColPKXMzyuYoHhOC5de4bY9m4327Z0s3VLN2OZIgCLOxu47e4LuWjDMtauW0LgFKyGOBNmJCop5Shw/VHe7wNurW3vA9QkM8URFAsVdu7oY/vWHt7f1sv723opFj1X/JbWOBsuW8669UtZt76ThsbYaa7t9FAzKhQnnWrVpmvvELt39bNrRz87tx/kQNcwUoIQsGRpI9ffdB5r1rZz7toOmmf5YeypRolKMatk0gW69g6xb88Qe/cMsnf3IAf2DeM4LgDRWJBVa9q4+tpzWLVmEavPXUR4HrjSTId5L6qnn3iH7Vt76FzWyOIlDSzubKCpJa4cDU8iUkoy6SI9B0boPjDCga4RDnQNs3/fMOnUIZeTZH2E5Sua2XDZcs46u4WzV7bS0paYEyN0J5N5L6rRkRxv/WYfzz69deI9w6/T2lbHovYkbe11tC6qo7UtQUtrgubW+IxmIJ8pOI7L6HCOgf4M/X0Z+g+m6e9Lc7AnzcHeFPlceaJsIGiwpLORiy9dztLlTSxd3sSys5qpS56Zi4UvGH+qbLZEz4EReg6M0nNglIM9KQ72pOjvS1P5kJ9Toi5Mc0ucxuYYjU0xGpui1DdEqW+MUl8foa4+QijkX7AtarVqk0kVGB3NMzqSY2Q4x+hwjuHBLENDWYYHxxgeyk102cDz22pqjtHWnmRRe5L2xUk6ljSweEk9jc3x0/ag9XRxRjspSilJjebp78sw2J9hoC/D0GCWocExhgazDA9lKdVGnQ7HNH0k6sIk6sLEEyHiiSCxeIhoNEAkFiQSMQlHAoTDJsGQn3DYJBA0CAT8mAHjpF5kUkqsqkO5XKVcsigWqxSLFQr5CsVChUK+TC5XJp8rkx0rMTZWZCxTJJMukEkXj7Ay4/h8Gg2NURqbYjS1xGlqjtPSGqe5NUFLW4Lmljg+38mZgDofOaOdFIUQnhVqiHLu2o6jlinky4yM5EmN5BgdyZNO5RkdyTOWKZJOFUin8uzfN0R2rES5bE3puH6/D9P0YZg+/IaOz9Dx6Z7zoa5raLqGJgQIbwRsvG2TrsR1JY7j4jgutu1gWw5WLVUqFpWyxVTaQl3XiCdCxOJBYvEgy1e0EE+ESCbDJBsiJJORmoWOEE+Ezzhrc7JY8KKaCuFIgHAkwJIpLMJcrdoU8mXyuQqFgmcNSiWLUrFCqWRRLlUply2qFdtLVRvLsrGqDnZNJK4jcV0X1/WU4boSIbwGQAiBpgt0zROf7tMwfDqG6cMwdEzTwDR9mAED0zQIBA1CNY/gcMQkHDaJRANEogECAWPBdmHnMkpU08Tv9+FPRj4SCEShGEeNOysUs4wSlUIxyyhRKRSzjBKVQjHLKFEpFLOMEpVCMcsoUSkUs4wSlUIxy6iHvwrFNEhli7y+veuYZZSoFIop8tirW/nao8demhRU90+hmDLrzlrE799xOT/6Dw8cs5yyVIozBttxKVWqBPwGhk9nV88QW/b2cd7SVlYvaT7u95e11rOstf645ZSoFPOaqmWTypXQdUFj/NAk51+/v58X39nDZauXcP26FWzc2c2zb3+ARPLxC89mZXsjb+w4QMDw8c6eg5SqFhetaEdKOeOZ/UpUinlLrlThsVe38kHPMC3JKNecfxZrl7Wyq2eIfX2j3Hn5GnYfHOHZt3cR8BtcvXYZbckYO3uHGHovj0/T+MS16/jVlj1s6+rnohXts1IvdU+lmLdEgya/c+PFfP0zt7KyvYl9A14o6IF0jny5ynlLW1nUEGf7/kH8Ph1d04hHAkhXoglBtlgBoC4aJFfbng2UqBTznq37+hnM5Ljr8nMBqIuEyJdqgokEEQLi4QD7B1KUKjaDmTzrz+4g4Pfx5Jvv817XAFes6QSYFadOJSrFvKZnOMPPXtvG2mWtdA+leXt3L6s6GulsruMvHnuFZzbt5J4r19JWH6c/leVnr22lJRmlJRnl5otXkStWWNqS5MJZ6vrBGRD4RTF/KJar7B9Msa8/xd7+UcIBP797yyWTlpdS8vAzv2HL3j4uWtFOazLGWLHMJ665gHypwge9wzTEwyxuqpv1up7RgV8UcwvbcelPZekZztA9mGb/YJoDg2n2D6YYTOcnyhk+nUvPOfaif0IIfu/WS4/6WSRozqr1mQ5KVIpZRUpJplCmf3SMgyNZDo6O0TeSpXdkjIMjY/SPZrHdQ/EEwwE/S5rrWH92B53NSTpb6ljeWk97YwLfPI0yPO9F9bPXtvH2B70010VoqovSlIhMpGQ0NG//mLmIlJKxQpnhsQJDmTxD6RxDmTyD6TwD6ZyXUlnK1SODl8bDAdrqY6xa3MQNF66goylBR2OCxU0JGmLhBRfxad6LKpUtsq2rn+ffyWPZzhGfCeGNBDXEwySjIZLRIPWxMHWRIIlo0MvDQeLhAPFIkGjQPKNEKKWkUK4yVigzViiRKZTJ5EukcyVSueJEnsoVGckWGM0Wj/ob18fCNCciLG9NcuWaTlqSUdrq47Qmo7Q1xIkGzdN0hqeHBTNQ4bqSTL7EYMZrPUdqrelItsDoWJHRbIFUrkQqV6BiOZPuJxI0iQZNoiEvjwT9RIImIdNPOGAQCvgJm36CAYOgYRAwfQQMH6bfh2l4ye/T8Rs+DF3Dp2v4dB2frqFr2rQCVkopsV0Xx5HYjhc30HIcLNuhajlUbYdy1aZiealUsShXLUpVm2K5SrFiUShXKJS9PF+qkitVyBUr5EoV8sXKEV2xw9E1QV0kSDIWnmiMGuJhGuNhGuMRGhNhmhJRGuNhjDMwcu0ZMVChaYJkLEQyFuKcxceex1WqWKTzRTL5Q61ztlBmrFAmWyyTLVbIFsvkS1X6RrMUylWK5Sr5UnXSi3A66JqYCJwp+FCEWrwotY50pxSF9lgIAWHTTzjoJxzwGodEOEhHY4JYyPReR4LEQgESkcCE1a6LhogGTRWx9gRZMKKaDkHTIGjGaauPT/u7lu1QKFcpVa0Jy1Cu2pQtu2Y9vNyyPUtiOe6ElXFdiVOLTOtKiZTSE1Ftvtn4JaxpXkhoXRuPVCswatbO8OkYPn3CGvp9OoGalQz4DYJ+H0HTs6gBw7fg7lfmA2ekqGaC4dNJRIIkCJ7uqijmKGfOXblCcYpQolIoZhklKoVillGiUihmGSUqhWKWmZGohBD3CSG2CyFcIcRRH4TVyt0shNglhNgjhPjSTI6pUJwOpJT0jI3xi507+M8vvXjMsjMdUn8PuAf4zmQFhBA68G3g40AvsEkI8YSU8v0ZHluhOGmMlctsHRzg3cEBtgwM8O5AP6OlEgBB37FlMyNRSSl3wHG9JTcAe6SU+2plfwLcCShRKeYEY+Uy24eH2D40xLahQbYNDnBgbGzi8+V1Sa7pXMr5La1c2NrK2fUNGH/4x5Pu71Q8/F0E9Bz2uheY1PNMCPEQ8BDA4sXH9qdRKKaDlJLebJYdI8PsGB5mx8gQ24eGOZjLTpRpi0Y5r6mZ+9acx/nNLZzX3EzMnN6E4OOKSgjxPNBylI++LKX8xRSOcTQzNumsNinld4Hvgjehdgr7Vyg+QqZc4oPRUXaNjLBrdGQiz1ergHdRdibqWNfayoNr17KmsZk1TU0kgzOfKXNcUUkpb5jhMXqBjsNetwN9M9ynQoGUksFCnr2pNHvTo+xJpdibSrEnlWK4WJgoF/WbrGxo4O5V57CyoZHVjY2cXd9AyDBOSr1ORfdvE7BCCLEUOAh8Ajh23FyF4jDSpRIHxjLsz6TpSmfoyqTpSqfpyqQpWtZEuYjfz1nJJFcv6eTs+npW1Ndzdn0DrZHIKZ1YPCNRCSHuBr4FNAJPCSG2SClvEkK0AQ9LKW+VUtpCiD8E/gXQgb+TUm6fcc0VC4aKbdOXy9GbzdKbHaMnO0ZvNsv+TIbusQzZyqGYfJoQLIrGWFqX4OJFi1iaqGN5MsnyuiRN4bnhRbxgnBQVcxPbdRkpFhjM5+nL5Rio5f35HAezWfpyuSO6agA+TWNRNMrieILF8QRLEnE6E3V0JhJ0xOKYxxnSPhUsaCfFd/r76M1maQyHaQiFqA+GiAcCaHOgxVqoSCkpWBapUpGR4qE0VMgzXCgwXCwymM8zWMgzUizifqjhNnWdtmiM1miUazo7WRSL0R6L0x6LsSgaoyUSQdfm72SfeS+qn76/nR+/t+2I93QhSASC1IeCJAIBEoEgdbU8EQgQD5jEzABxM0DMNImZJlHTJOr3Y+hnjmu447oULItcpUK2UiFX9fKxcpmxSoWxcol0uUymXCZdKpEpl0mViqRKJSrO0UMS1AeDNIbDNIcjrGzw7meaI1GawxFaoxFaIlHqAoE50U07Wcz77l+2UmYgn2e4UGSkWCBVKjFaKpIueRdAplwmXS6RLpXJlEtYx3GHN3WdiN8k4jcI+/2EDD9hw4tHETYMAj6DoOEj4PNh6j5Mnw9T1zF9Pvy6PpF8moZP0zA0LzaFr+bNqwmBLrxWWAgQiA+500ukBFeOu9RLnFqsivFkOS6W61B1DqWKbVOupYrj5SXLomTbFC2LolWlULUoWhb5aoWCZU0ML0+GAOKBAIlAgLpag5QMhqgPBakLBKkPhSZENN5LOFMapQXd/YuZAWJmgLOPv2wQUkqKllVrhctkK2Wyh7XS+WqVXKVCvmpRsKoUqlWKlkW6XKIvl6NoWZRtq5bbkz9sO834dZ2QYRDw+Qj6DEK1RiEZDNIRjxPx+wkbfiJ+/4SFjprmhOWOB7ztqGmqbvQJMO9FNR2EEIT9fsJ+P23R6Iz2JaX0LIRjU7EPWYxxC2K7LlXHwXFdbFdiuw6uBFe6uLIWo+KwfR3eHdJrQWH0mmXThMCn6fi0WqwKTTvCIpq6ZyUDPs9yKiGcXs4oUc0mQgiv6+fzwZkV1k5xHObvEItCMUdRolIoZhklKoVillH3VArFNCg7VfbmBo9ZRolKoTgKUkoGy2PsyQ2wJzfA7lw/u3MDdBdGcI/zMEWJSnFGI6VkpJKjKz9EV36IfflB9tZSwT40kbc1WMeKaAs3tJzHilgr1/GNSfepRKU4I7Bdh4OlNN2FYfYXhtmfH6YrP8T+wjB5uzxRLmYEWR5p5ubWC1gebeasaAvLI81Ejak7LypRKRYMtuswWB6jtzhKT3GU3mKKnsII3cUReospHHloilq9GaUz3MDNbefTGW5iaaSJZZEmkv6Z+14pUSnmDVJKcnaZ/lKag8UUfaU0faUUvcXUxOvDhWNqPjpCDSyLNHNN0xqWRBpZEm5gSbiR2DQsz3RRolLMGSzXZricY6gyxmBpjMHyGAPlNP2lDAOlDAPlzBH3OeB119qCSc6OtXJd87ksCiVpDyXpCDfQaEbRxKl/aqREdYZRcSwMTZ+42BzpMlLJIYCmgLdeV18xTcmpEvGZNAcTFO0KW9L7CegG6+qWTrt7ZLk2qWqB0UqO0UqOkfFUzjJcyTFcyTJcHiNVLXzku1FfgOZggkWhJBcll9EarKMtVEdbsI5FwSQRIzDj32S2mfei2po+wMFSioQRJu4PETdCxP0hwrq5oH12ToTe4ihffOdRvrD6di6o68SVLhtH9vBM3xaiRoDbF11Ee6ie7+19kdZggqJT5Y/OvpmXh96nKz+EqRnk7QpXN51z3GP9X5sfoacwwmg1T9YqHbVMnT9MoxmjwYxyTmwRjYEYjWaM5kCc5mCc5kCCsG/+Tayc96J6qu8dHu/Z+JH3daERM4JEfUFiRpCIESDqCxAxgkR8AcI+cyIP+wKEdD8hn0lQ9xPy+QnqfgK6H1NbGKsRlh2Ln/ds4q729diu52BYtKs8N7CVr55/P3m7zP+740k+tfRqOkL1/M7ya/je3hfZnRvgzZHd/Oe191NxLL6+/fEpiSqkm3RGmrjQv4ykGSHpj9BgRqk3ozSaUZJmBEOb95ffUZn3Z/VHK2/mgc4ryVQLjFlFxqpFxqwiWavImFUib5XIWmWyVom+Ypq8XSJvV6i69pT2ryEwdYOAbmBqhueYqBn4NR9+zYeh+fBrOobmw9B0fELH0HR04Tkm6kL3XDeEhsBzUJxY6xfx0aiIEly8pUtdZM1NxMU5LNmugy1dbFlzNXFtvnLuvST8oUnP451UF2fHWik5FiXHi0CkCUHV8X4HQ+hUXZuiU52wDmHdpOxYODXHTl1oH3GNn4yvnn//lMotROa9qCK+ABFfgCXhhml9r+raFOwyRbtKwS5TsCuUnCoFu0LZsSg6Xl52qpQci4pjUXYsqq5FxfW8a6uuRd4uYbkOlmtjS88j15IOTu3CHxeEXfPiPd7T+MPR8PyqNDx/Kk+c44LVMYRe8y72YR2nkdic6sKSDrtz/SSMEBvql2NoOg2BGAeLKfJ2mY5QPS2BBE8VNrM3N8jBUorbFl3E8mgLrw7tpOJarE2oqMHHY967089HxsU12W8/bs1OBs/2v0vCH+bZ/q185dx7OFhM8cOuVzA1H7+z7BqSZoSfdr9Jwa7QaMa4ddE6MtUCj/dswq/5uLvjYkLz8D5ntjmWO70SlUJxAhxLVMr1Q6GYZZSoFIpZZt4PVCgUp4qSPUaqeoDRyoFjllOiUigOw5UOWWuAdLWHdLWXdKWbVNVLZSd7/B2gRKU4A5HSJWcPM1btI1M9SMY6SKbaS7p6kLFqHy6HHk8E9QR1/nbOilxJnbmYev8S6szF/PujLtnmoUSlWJBUnAJZa4CsNcCY1U+22s+Y5aWsNYAjDy3BowuDhH8RSf9ilkUuo87f4SWznaAen/axlagU8w4pJUUnQ84aJG8Pk7UGyVlD5KzB2vYgZTd3xHf8Woi40UbSv4RlkcuIG23E/W0k/IuI+hoRszibXYlKMaew3SoFe5SCnarlo+TtEfL2MHmrltsjR1gaAEMEiBrNRI1mWoKriBmtxIxm4kYrcX8rphY9ZXM4lagUJx3LLVNyxijaaUqLqu/HAAAKc0lEQVROhqKdoeikKdkZCk6Kop2maKco2GkqH7Iw4HXPwr56Ir4GmoOrOMvXRNRoJOprImI0EjOaT6lojse8F9WB/CZGKl0E9CimHiWgRTD1KKYewdTC+LXQtEz7YGkXrw8/TNzfxorox+gIrUMIQdYaZOPI32PLChvqP0nSXMzm0X+i4KQwtQgX1z9AycmwcfRH2G6FDfUPEvNPfjM735BSYssyFadAxS1QcXKU3byXT6TsEankjFFystiyfNR9GiJAyJck5KsjaS6hPbSOsC9J2FdfyxuI+OoJ6LE5I5ipMO9FtSf/Ou9lnjxGCYFfC+LXwgT1GA8s/c4x9yeR6MJP1S0SNZom/szNqX9iQ/2D+DSTTaM/Zn39b5Ozh9nQ8CCbRh6l6GR4J/VT1sRvRhcG2zJPclnj/44mTt3SMlK6ONLCkRa2rHq5W8GRVWxZxXLL2G4FW5axJvLxVMJyS1TdElW3UMuLte0iVaeAy9HXpBrH1KIE9BhBPUrIl6Te7CToSxDU4wT0OCE9QdAXJ6TXEfIlMLST59J+Opn3orqu+Y+5qvEhym6u1mrmKTtZqu54i1qY2Jby2BcFQHNgJXd2fI2SPcarQ9/h+tb/A134KNkZIkYjmtApOWNkrUFiRjNBPU7c31a7Se6nwVyOEIKcPXTcYznS4qcHPn/EexKQeK4WUrreelU4uNJFSgcXB1d6SeLgSBtX2jjSmvje9PEaHkMLYogAfi2EoQWJGU34a9ber4cxtTCmFsGvh4/oEQT1GH4tfEobkLnMvBeVEAK/HsKvh8BonpX9AQR9capuEV14P5FPM3GljSZ0dGEQ0hMUnQwARTtDUI+hC/+h/XiOG8c9nqlHkMgPldU8fyuhe4vCoaEJDYGOJnSE0NGp5cKHLgy0Wj6+7RN+dGHg00x8wsQn/Pg0E134PfFoAXzCxK8F0YV/XnWv5jrzXlSzzb7cr9lf2EjFyXN+3Z082/dn3Nj2RS6ou5tfDf41UkrW1t1B3N+G41Z5fehhbFkhZrRwXuI2fjX4V0hgdfzm497L6cLgro5vnpoTU5wylOvHJEjpIoSGI+0Ja2W5ZSQSf+1ewHJLONJGoGHqYW+BaXsUF4eor0m1/guYBb086cli3MqMCwrA0I6M3GNoQYwjviOIGNPzQFYsPJSoFIopImUF7APgdB2z3IxEJYS4D/hPwDnABinlUftqQoj9QA5wAHsys6lQzAYfXkN5Wt91i+D0gNMNTjfS7gbngCcmtw+mEGNkppbqPeAe4NgPfzyulVKOzPB4ijMMKasgbRA6QnixMaSbB2sbaBGEcR5SlqDyJsgx0DsR/guQ1i5k8VGErxNCDyIOG5k9Gm7ur6H0E3A/dImKBPg6wH8hwncP6EvB1wmcN+m+ZiQqKeUOQN2QK04K0hlA5v8ahIkwbwDzipqAnkda2xFaHCnLoLUgK79C+NcjKy+DbzFUXkAE7wZ3FIqPQPgzx7RgQl+ENK9B6B2gd3j70JcgtLk7S10CzwohJPAdKeV3JysohHgIeAhg8WIVDutMRUoXKi8DLkJrg3FL44wiqxvR4l9HOkPI/F8gQp9EGKsRwTug8H2wdiKdXjT/BZ4wKy8e94mhCN2L4N5ZqftxRSWEeB6O6pH1ZSnlL6Z4nCuklH1CiCbgOSHETinlK0crWBPcd8EbUp/i/hULEOkMIMybPAuV+TzCfzEIA2TVKyBMGJ+tLmuOhdICEYbx2TMiyFTug2aT44pKSnnDTA8ipeyr5UNCiMeBDcBRRTX9fZcAH0IYxy2rODlI6YLMgzsGMlvLx7zcTSPdMZAZcNPgerkI/1tE6FiWQXhdMRzveyLi7UeLgd6BrG709uNfD3ob0v4xlH6BdIcQxhqEeSVu9pvefoL3eXtcKK4fQogwoEkpc7XtG4Gvztb+Ze7PofgIUgRBRL2kxUBEQIt4uYggtIjXgk2kkNeKidBh2+MpMKtOa3MN74F/BWQZZAlksZaPbxfBLYIsgCwgZR7cgiccmQM3V8vznohknmNaAxEEEQetDrQEGKtBP/bzPCEEMnAjMvd1sN5BmFcg899Ci30FQr+NLP4YocVqgxABCNwMsoII3okQPmTgJoS+GLQw6Mtn9fc7HjOaUSGEuBv4FtAIZIAtUsqbhBBtwMNSyluFEMuAx2tf8QGPSim/NpX9T2VGhay8DtaWWmuYr/3htT/azdcuhIJ3oUwLA0SglkzA7+XCX9v2e10RjFruq+U6CF/tVHUQOl4kuPFc1FrMw9MRZwS4tQt/PDmAW+vSOIBd27Zr3R7rsNwCql4XSVZr25XDUhmoML0ukVFrpMKHNVyRWh4FEa81WgmvQdPiNRF5QhoftVtIqAi14M1Ql6WayGqtsFs81DLLSk14ZZBlr1t5xIU4fnGOX6zWYRft4Re2U7uwXQ5d/K73/oRIpoN2KAkdT5y+mnDHt43aa6Mm+lou/IB5qDEQJhCoWeLxBuNwCz1utcPea82z6scbjj4TUdOU8GZ8IyJAZGrlT1I9jrRA4wKTHzri4RZNMd84Y0Q1VzjU9VMsVBbu3bhCcZpQolIoZhklKoVillGiUihmGSUqhWKWUaJSKGYZJSqFYpZRolIoZpk5PU1JCDEMHHvZOmgAFoJH8UI4jzPpHJZIKRuP9sGcFtVUEEK8tRBiXiyE81Dn4KG6fwrFLKNEpVDMMgtBVJPGu5hnLITzUOfAArinUijmGgvBUikUc4p5JyohRFII8ZwQYnctr5uk3H4hxDYhxBYhxOlZ5eBDCCFuFkLsEkLsEUJ86SifCyHEX9c+3yqEuPB01PN4TOE8rhFCjNV++y1CiP94Ouo5GUKIvxNCDAkh3pvk85n9D1LKeZWA/wZ8qbb9JeDPJim3H2g43fU9rD46sBdYBviBd4HVHypzK/AMnhfjpcBvTne9T/A8rgGePN11PcY5XA1cCLw3yecz+h/mnaUC7gR+UNv+AXDXaazLdNgA7JFS7pNSVoGf4J3L4dwJ/FB6vAkkhBCtp7qix2Eq5zGnkV7MydQxiszof5iPomqWUvYD1PKmScqNR8V9uxb19nSzCOg57HVv7b3pljndTLWOlwkh3hVCPCOEWHNqqjZrzOh/mJMxKo4VFXcau5lyVNxTxNECU3x46HUqZU43U6njZrxpPHkhxK3Az4EVJ71ms8eM/oc5KSp5jKi4QohBIUSrlLK/ZpKPumK1PIlRcU+QXqDjsNftQN8JlDndHLeOUsrsYdtPCyH+VgjRIOfPqi8z+h/mY/fvCeDTte1PAx+J5y6ECAshouPbeFFxjzrScwrZBKwQQiwVXiC9T+Cdy+E8AXyqNvp0KTA23tWdQxz3PIQQLaIWX00IsQHvOhs95TU9cWb2P5zukZgTGLmpB14AdtfyZO39NuDp2vYyvFGpd4HteIspzIW63wp8gDd69uXae/8O+He1bQF8u/b5NmD96a7zCZ7HH9Z+93eBN4HLT3edP1T/HwP9gIVnlT4zm/+DmlGhUMwy87H7p1DMaZSoFIpZRolKoZhllKgUillGiUqhmGWUqBSKWUaJSqGYZZSoFIpZ5n8BGCbloCSa1s4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output(SGDOptimizer([w], lr=0.33333), fname=\"sgd_lr_opt_example.pdf\")\n",
    "output(SGDOptimizer([w], lr=0.1), fname=\"sgd_lr_good_example.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9oNyEHXyQ23T"
   },
   "source": [
    "# Momentum\n",
    "\n",
    "We can slightly fix the above problems by adding Momentum to our Optimizer. \n",
    "\n",
    "Recall from the lecture that Momentum add's a certain \"force\" to the direction we were travelling in before. Intuitively, from a physics perspective our optimizer has a certain momentum built in when travelling through our scary loss landscape. The benefits of momentum are as follows:\n",
    "\n",
    "1. Accelerates Optimization. Emphirically this has been observed when we train neural networks. However, no **theory** confirms this. We can however theoretically confirm this for quadratics.\n",
    "2. Noise Smoothning. Momentum can help skip over local minima and help aboid the draqstic direction changes as we had seen in vanilla SGD.\n",
    "\n",
    "Recall the equation for SGD + Momentum was given by:\n",
    "\n",
    "$$\n",
    "v_{t+1, i} = \\beta*v_{t,i} + \\frac{\\partial{C}}{\\partial{w_{t,i}}}\n",
    "$$\n",
    "\n",
    "Here, $\\beta$ is a hyperparamter we have to tune. A popular choice of $\\beta$ is 0.9 which intuitively says that we care more about the past directions of the gradient than the direction indicated in the current step. Using $v_i$, our weight update step becomes as follows:\n",
    "$$\n",
    "w_{t+1,i} = w_{t,i} - v_{t+1,i} * lr\n",
    "$$\n",
    "\n",
    "\n",
    "**Note**: $v_{t, i}$ for $t = 0$ is 0.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "sEr15GJ3ZC7i"
   },
   "outputs": [],
   "source": [
    "class SGDMomentumOptimizer(Optim):\n",
    "   \n",
    "    def __init__(self, params, lr, momentum):\n",
    "        defaults = dict(lr=lr,momentum=momentum)\n",
    "        super(SGDMomentumOptimizer, self).__init__(params, defaults)\n",
    "\n",
    "    def my_step(self, p, state, group):\n",
    "        lr = group['lr']\n",
    "        momentum = group['momentum']\n",
    "        d_p = p.grad.data\n",
    "        \n",
    "        if 'v' not in state:\n",
    "            state['v'] = torch.clone(d_p).detach()\n",
    "        else:\n",
    "            state['v'] = d_p + momentum*state['v']\n",
    "\n",
    "        d_p = state['v']\n",
    "        p.data.add_(-group['lr']*d_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jt462ngbWRH9"
   },
   "source": [
    "Let's visualise the performance of this optimizer below. We see that SGD + momentum can perform  better after tuning the learning rate and momentum !\n",
    "\n",
    "An important point to consider when measuring the effect of momentum is to change the learning rate by a similiar amount. This can be achieved by something like this:\n",
    "\n",
    "$$\n",
    "lr_{new} = lr_{old} * (1 - m)\n",
    "$$\n",
    "\n",
    "Unfortunately, tuning these hyper params is a real part of training neural nets effectively :("
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "id": "n9eN7lQFcKLL",
    "outputId": "e94cc645-f3d8-4891-f579-f4bf6b69d2f9"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nQ2d2mMewVAYG3cAUnxzdYZ5e6ouBwVGDYamOACp9Pp5fvpRyr5fj+xZy+ajRmE0mav1+nlr8LZ5wmFsmTmZgejpvrlnFLp+PFJuda8eOIxyL8dyyJfgjEX407lhy3UkH+3AOewxRxZFSEohGaY5E4imMPxolEI3ij0QIxD+HVJWQqhJU9c9hNUY4pgcrhtUYUU0jEouhai2hGRoxTaJqGprUiEmpBynGt3sihB5hZRICxST424zTmZif32Hf85KSuGfKVIQQ3PXl50RiMcwmE88sXcKlx4zGbbXyyqoVXDduPJvq67lmzDheWrmcxlCIt9euYUxOLjazmf+uW8cN4ydgVQ7+hNXDmSNOVJqUNIVCNAQDNASDNAaDNIaCNAZDeMIhmkJ68oZDeMPh1tQcibR7kreHIgQOiwWbougRtmYFq6LocVaKgkUx4TDbMJtMWBQ9elcx6UGKLVG8JtEioL37L+PbmKaRbLN1qU/zd5bx+LeLuGjkMdjioqj2N9M/LQ2rolDj91Pm8ZCflExRair9U9PY5fOyrraGm8ZPQDGZeHPNajqLWqjwelFMgnSH0xDfPjjsRfXaqpXM2rKZukCAukCAxlBwn+KwKgqpdjupdjvJNjt57iSGZmSSZLORbLORZLXhslpxW624LFbcVgtOixWX1YLDbMFpseCwWLCYEht8mAhOKCzihMIibvrwfS4cMRIAm6K0ikQRgjSHA09YD7fwhEO4rba4Rfz+1trUyXHdPfsLvi7T171LstrIcDrIcrrIdDrJcrnIcrrIdrnIcbv1rctNqt1+yP29epLDXlTecJhANEphSgrj8vLIdDpJdzhIdzhJszvIcDpItTtIs9txWA7P4MTOWLKrgk83byYSizEpv4Bffj6Lv804javHjOOPc+egScmFI0YyIC2N5kiExxYtpC4QoG9yMheNGMlfvpkHwMxBg7F0Yn1umjCRUwcOoiEYpD4YoD5+MdtYX8c3ZWX4IntHXdsUhRy3mzx3ErluN3lJSfRJSqZPUhJ9kpLIT0omqYsW+XDACFI8QtBD7SUmIQirausFpDEYJCYlGQ4HQgjqAwGCahSLST/RY5rG+rpaVE1jZFZ2p6LqjJAapcbvb01Vzc1UN/uobG6mqrmZSp+Pan8zqrb7ehspNhsFySnkJyfTNzmFvinJFKakUpiSSkFy8iE31DSCFI8C9FB7fYjV1iKnOXZ/K2GG07nbd8Vk4pjsnIT1w262tIphX8Q0jbpAgF0+LxU+HxVeLxU+L+VeL6WNDczdvo1w7PupQCYhyE9Kpl9qajyl0T8tjQFpaeQnJe82fD0UMERl0OsoJhM5bjc5bjfj8vbeL6WkNqA7Vso8HnY0NbKtqYntTU0s37Ce5kikNa9VUeifmsbA9HQGpqUxKD2DQekZDEhLw2Y+OKd3QloVQrwAnAXUSCmPaWe/AB4DzgACwLVSymV75jMwAN3qZrvcZLvcTOiz++MEKSV1gQDbmhrZ1tjI1sYGShsbWVtTw6wtm1udVCYhKEpJZUhGBkMzMxmakcnwrCwKU1I7dcYcKImS8ovAE8DL+9g/ExgcT5OBf8a3BgbdQgihexldLibl7/5anLCqsq2pkc319WxpqGdjfT0b6+v4fOuW1oB7p8XCkIwMhmdmMTwrm5FZWQzNzMJpsbBw4UJKSkqYNm0axcXF+93HhIhKSjlPCNGvgyznAi9L3SuySAiRKoTIk1JWJqJ9AwMAm9nMsMwshmXuHgUcjEbZFBfYhrpaNtTV8vHmTbyxZjWgW7X0unpWPPAgsVgMi83Gp59/zklTpuxXP3pr0JkP7GzzvTz+216iEkLcCNwIUFhY2CudMziycVgsjMnNZUxubutvUkp2+Xysq61hbW0Nrz/1T2KqigaEI2Eu/OtfmLijlDE5uYzJzWNcbh6DMzIwd8Ep0luiam8Q264vX0r5DPAM6C71nuyUwdGLEIL85GTyk5OZMXAQk6XglFdfIwKYrTauPPtcvO4kZm8r5Z11awFwmM2MzsllbG473pU29JaoyoG2ccsFwK5eatvAoFOKBwxgtpSUnHEG037zm9Z7KiklO70elldWsqKqkhVVVbywfGmHdfWWqD4AbhVCvInuoPAY91MGhxRLl1IMFN9xB7RxUgghWp+7nTtsOKA7ROw/u22fVSXKpf4GMA3IFEKUA78nvti3lPJp4BN0d/oWdJf6jxLRroFBwliyBISAceM6zdrZ869Eef8u62S/BG5JRFsGBj3C0qUwZAgkHXg82aE1v8PA4GCxdCmMH5+QqgxRGRhUV0NFBUxod35stzFEZWCwNO7NS5ClMibU9jBSStRYPKw+pofWa5r+3t92w+nRw+iFECiKHi2sKCbMiumQm419xNANJ0VXMEQVR9Mk/nAErz+ENxDCFwjjC4ZpDkbwh8IEQlGaQ2GC4SiBeAqGo4QiUUIRlXBUT5GoSjgaIxqLEVVjxLTEPb8WAqxmBYuiYLWYsVoUbGYzNqsZm8WM3WrGYbXgtFlw2C04bVacNgtuhw2X3YrbYcXtsJHksJHstJPstJHktGNWjnKxJtBJAUewqKSU+AJh6rx+6jx+GnwB6r0BGnwBGn1BGpsDNDUH8fhDNDUH8QbCna5RYbMorSeqw27FbjFjt1rITLFhj5/YLSe6xaxgMSuY41bGbNK3JpPAZGp5qTa6Utr2W9MtmKbpQYe6ddNQYxpRVV9MJhLVBRtWVcJxQYciKqFIFK8/pAs+EiUQihAId/zuXgC33UqKy06K20Gqy0FakoM0t4P0JCfpyU4ykpxkpLjISHaS5nYeeSJcuhSmTUtYdYe9qFaVVrJ2exVVjT5qmpqpbvRR5/FT62kmHN17zWuzyURq/KRJdTsYXJBFqstOisvReuVOdupX8pYru8tuxeWwHnBU7MFA0yTBSJTmYDieIviCYbyBUNwqh/H4Wy4uIZr8QbZVNdDYHCAUUfeqzyQE6clOslPdrSk3LYmctCRy05PIS08mM8V1+AivxUmRoPspOAJE9eniDbxVsgKrWSE7zU1OahKj+ueRmeIiK8VFZjylJznJSHaR7Dz8X9TcHUwmoV8U7FZy0ro3vAmGo9R7/TT4gq0Wv+WCVdPUTHltE0s2ldMc3H1dCsUkyE5N4qVfX0pmiiuRh5N4EuykgCNAVDfMnMyNZ0wm1e04qsTSGzhsFgqyUinI2ndoPIA/FKG60UdVo4+qBh+76r1UNnhJcds7LFfT1Mx789ewcWcNJ48bzKkThrSOBpZuKmdXvYeJQwvJTU/CH4oQiarYbRYc1gQu4JNgJwUcAaJKT3Z2nsmgR3HZrQzIy2BAXvuvEN0X2alurjjlWKSUvDDrO7ZUpDO8MIc5K7awq95LKKJSsmorF0wZxaffrWdrZQPhiMrVM8bTNzuVV75Yyrqyai6ZNpbxgws6b7A9EuykAOM5lcFBREqJy27ly+WbKchKJSdVP7EXrNtO8Ygirps5iYo6D8s2V9AcivDTc3/AiKJswlGVf89azNC+2fzqomks26xbtf1i6dKEPfRtwRCVwUFDCMHbc1dit5g59/iRraOOSDSG26GvAxiOqMQ0DbvFjFkx4bRbCUVVymoa6ZuVQlaqm5qmZtSY1lFT7dMDTgo4AoZ/BocvXyzdxP++Wc2wvtkIBOt3VnPLOT9g6piBlKzcSqrbTm56EsMLc/h2fRkef4htlQ2MGdAHh82CzaqfvmpMw23fj8U4e8BJAYaoDA4i048dTPGIIsJRFU1K+mQmY1ZMTBnVn8+XbKKmyc95xx9DmttB3+xU3ixZoS9vlpbEpSeN49mPvyWmaUwbM5BUt6PT9j76dh2D+2QyKD9Tn52ydGnCnRRgrFBrcBjj8YcIhCNkp7o7ncLl9YeY9st/AvrD7tED+vCr1x8hp6YS04b1WC3dsy/GCrUGRyQpLjspro7d9i0kOW18dN91rNhawYotu1i+pQL76lV81Wcg997+FKP692Hi0AImDOnLMf1zD+hBv2GpDI5OqqshN5fNt9/N+5NnsHRTOZsqapESnDYLxw4u4LjhhRw3vIj+uel7PQM1LJWBwZ7EnRSDzzmNX554IqAPJ5ds2sl3G8pYtL6Mb9ZsAyAnzU3x8H4cP7KIycMKSXJ2bB0NURkcnbTjpEhx2Tll3GBOGTcYgF31Hhau28Gi9Tv4cvlm3luwBsUkGDOwT4dVG6IyODpZsgSGDu1wJkWfjBQumDKaC6aMRo1prNleyfw12/k6bsH2hXFPZXB0UlCgh3u8+up+Fe/onsqYUWFw9NFDMylaMERlcPTRQzMpWjBEZXD00UMzKVowRGVw9NEFJ8WBYIjK4OgjgQtntochKoOjix52UoAhKoOjjR52UoAhqm5xKD/TM+giPeykgKN4RkUkrC+/ZbV9/ycIh6Ns31qL1Wam/8BsVDXG+jUV+P1hMjOTGDQ0l6rKJr74ZBUZWUmcdsYYFHPH1yVPU4Caag/RaIyYqqGqMX1Nv5iG1ORur5MUAEKgKAKTYtJXpjWbMJsVrFYzFouC1WbGbrdgs1uwWs3GYjfdZOHnn1OSmcm0NWsO6GXZHXFUimrjul288fJ80jPc/OxXMwFQ1RiLvtnM8iXbSE5xEgiEyclN5fNPVzFkWB5rV+8kvzCdr+esp7B/JtFIjE8+XM7Z53c8jJjzxVqefOSzHjkOIcDusOJwWHE4rbhcNlxuGy63HXeSneRkB0nJDlJSHaSkOElNc5Ga5iQt3Y3Dae2RPh3KLFy4kFPmzyciJdZTTmH27Nk9IqyjUlRDR/ThtjvP5F+Pf9H6m6cpwOJFW/nlPWfjaQrwzBNf8sNLJjNwUA5nnz+ed15fyNZNVWwrreWiy4vxNAX41xNfdiqqScUDycq+CItVwWw2oZgVlNaVagUCoZuouMnSV6fViKn62utq3LpFIzEiEVVPYZVQKEooFCEUiBIMRgj4w/gDYfzNYRrq6/D5Qvi8QaKRvRcUBbA7LKSnu8nISiIj001WdjKZWclk5SSTnZNMdk4KqWnOI8oSlrz3HhEpiQGRSISSkhJDVIlEmARam3XOzWaFaFQfElosCqoaIxbTEKbvTyrFrKDFFxix2szQhXusPgXp9ClIT3Dvu04oFMXbFKCx0Y+nKUBjg5+mRj+N9X7q63zU1zezaX0lC+ZtIrLHirQ2m5mcvFTy+qSS1yeNvPw08gvS6FOQTl5+Kmbz4bVi7zSbDSsQURSsVivTErjUc1sOe1GtW13OqhVllG2vpWx7PZOKB3L19VM7LafFNEKhKKoaw+cN4nLbyc5NYeO6XXi9QYYO70NObgqffLCcRfM3U1PlZeAFOYweV8QbL88nFtOYesrIXjjCA8Nut2DPTSE7N6XDfFJKvJ4gtdVeaqo9VFd5qK70UFXZRGVlE6tWlBEMRFrzK4qJPgVpFBZlUtgvk34Dsijqn0Xfogys1kPztCreuZPZycmU3HEH0046ybin2hdffbGG9/+zhMysJAr7ZZKR2flT8sYGPy88/RU11V7efXsxVZVN/PT20zn7/PG8+/ZinE4rF1w6GafLxvhJA/B5g/xg6lCsNjMnzRjJiqXbsdstjB5X1AtH2DsIIUhJdZKS6mTQ0Ny99kspaWoMsKuigYqdDewsq2fnjnrKttexcP4mtJhutU2KoG9hBv0HZjNwUA4Dh+QyaEgOaenu3j6kvZkzh+IZMyi+++4ebeawD/1obPBjtSq4Olli2KDniEZjlJfVs720lm1ba9hWWkPp5mpqqr2tedIz3QwZmseQ4XkMG5HPsBF9SErufAWkhLFtGwwYAE88Abcc+Ounj+hw+rT0Q3wB/KMAi0Wh/8Bs+g/M5qQZ3w+Jfd4gpVuq2bKpms0bK9m0oZJvF2xuvRXtW5TByFEFjBhVwDGjCyko3HstiIQxZ46+Pemknqm/DYe9qAwOXZKSHYw5th9jju3X+pvfH2bj+l2sX1PB+jXlzJ+3iVkfrQQgJdXJMWP6MnpsIaPHFjFgcA4mU4JENmcOZGfD8OGJqa8DDFEZ9Coul41jJ/Tn2An9Af1ebeeOetas2smalWWsXrmT+XM3ApCc4mDs+H6Mn9if8ZMGkJPX8dtH9omUuqimTdvrJXs9gSEqg4OKEEm/lu4AACAASURBVILCfroH8Yxz9KlDNdUeVi0vY9mSbSxfvI15X60HoKAwnQmTBzLxuIGMObYIm62Lr9TZulWfRNsLQz9IkKiEEKcDjwEK8JyU8i977J8GvA+0rJjxPynlnxLRtsGRR3ZOCtNPH8X000chpaRsRz1Lvy1lyXdb+eT95bz3zmJsNjPjJvSn+ITBFE8Z0rF3sRfvpyAB3j8hhAJsAmYA5cBi4DIp5bo2eaYBv5RSntWduo2FXwz2JByOsmp5Gd8t2MKi+ZuoqvQgBIwYVcCUacOZMm3Y3s/kLr8cSkp0a5Wg4V9H3r9EiKoY+IOU8rT497sApJQPtMkzDUNUBglGSsm2rTXMn7uRb+ZuoHRLDQDDRvThxJNHMPXk4WTnJEOfPnDyyfDaawlru6dd6vnAzjbfy4HJ7eQrFkKsBHahC2xte5UJIW4EbgQoLCxMQPcMjlSEEAwYlMOAQTlcdd2JVJQ38PWcDcybs55nnviSZ574klOKzNxZVUW4+AT242U7+0UiRNWePd3T/C0DiqSUzUKIM4D3gMHtVSalfAZ4BnRLlYD+GRwl5Bekc+lVx3PpVcezq7yBOV+sJfbkkwDc8spWBtS+y6lnjGbchP4oSs+FEiZCVOVA3zbfC9CtUStSSm+bz58IIZ4SQmRKKesS0L6BwV70KUjnih9NQX76ONGKPEZfeDIlX65jzhdrycpOYubZ45h5zlgys5IT3nYi7qnM6I6KU4AKdEfF5W2Hd0KIXKBaSimFEJOA/6Bbrg4bN+6pDA4IKSEnB04/HV5+mUhEZeE3m5j14QqWfleKMAmOnzKUc344nrHj+3VrNkeP3lNJKVUhxK3AZ+gu9ReklGuFED+J738auBC4WQihAkHg0s4EdaQipfw+Ajim6VN2Wv4UrVG/CmaLCVMnLzIz6IR166C2ttWVbrWamXryCKaePILKikY+fn85n364nG9KNlDUP5NzL5jI9JmjcDgOLIDzsJ9Q29tEwiqNtV6a6nw01TXjaWjG2+DH1+Sn2ROk2RPA7wsRaA4RbA4TCkQIhyKEghGiERV1H0GD7aGYTVisZqx2C3aHFZvDgsNlx+Gy4Up24E5x4E524E51kpLmIjndTWqGm9RMN2nZKTjdtiMqyLDbPPEE/PSn+mTafv3azRIJq8z9ah3vvrOYzRsqSUp2cO6FEzj3ggmkpu17XmmPutR7kt4WlZSSxlofVWX1VO2sp6aikZryBmorm6irbKK+yoOvKdBuWbNFISnViSvZgSvJrp/8bhsOpw2bw4LVbsFqs2CxmjFb49G/8QhgIQRSSqTU47xiMY1YNEY0ohKNqIRDUcLBCKFAhFAgTMAXJtAcotkbxNcUIByMtNsnm8NKZm4KGbkpZOWlkpWfRnZ+Orl908npm0F2fhpmy+EVaNgtLrgAli3TRdUJUkrWri7nndcWsuDrTdhsZk4/eywXXXZcu9OjDFHtQUyNUV5aS9mmKsq2VFG2uZry0hp2baslFNj9BE3JcJOVl0pmXioZuSlk5KSQnp1MamYSqVlJpKa7SEpz4XAdPKsQCUXxNQXwNvppqvPRWOujodZLY42XuioP9VUeanc1UlflaY1cBjApJnL7ppM/IJvCwTn0HZRD0ZBciobk4XD1lgO6h9A0yMqCc86Bf/+7W0V3bK/jndcW8uWs1QDMOGM0V157wm7iOqpFFfSH2bqmnC1ryildV8HWdRWUba5qHYYJIcgpSKdgUDb5/bPo0y+L3MIMcvumk12Qjv0Ax9eHEjE1Rl2Vh+ryBqrK6qncUUdFaS3lpTWUl9YQDX8fTp/bN4MBI/MZMKIPA0cWMHhUXzI6iR4+pFi5EsaOhZdegquv3q8qaqo9vPPaIj5+fxlSSmaeM44rrj2BjMyko0dUmqaxY2MVa5eUsnH5DjauKKN8a03ren2pmW4GjMhnwPB8iobm0m9oHgWDco4o4ewvsZhGVVk9OzZVsmNjFdvW76J0fQW7ttW1/v3SspIZOraQIWMLGTG+P0PHFR26f7tHH4XbboOyMujbt/P8HVBT7eH1l+Yz68MVmM0mzrtoEjfccsqRK6odGytZOm8DqxZuYe3ibTR79HuelAw3Q8cUMmRMIYNG9WXwqALScw6jK+0hQtAfZuvaCras3snmVTvZtEq/UIF+Hzl4dF9GHzeIUcWDGDmhP3bnITJsPPdcWLsWtmxJWJW7yht4+bl5fPXFGr5Y8NsjV1SP/fpNZr25iPz+WYyaPJCRkwYwcuIAcgszjm7PVw/iawqwfuk21nxXyprvtrJpZRkxVcNsURg+vh/jThjKsVOHMeiYgh6dubBPYjHIzIQLL4Rnn0149Vs2VjF4WN6RK6rqnfUoFoXM3P0MYDM4YIL+MOuWlLJi/mZWfLOJrWsrkFKSnO5i4kkjKD71GMZPHdZ7VmzZMn2t9Nde02eo9wBH9BoVOX0zDnYXjnocLhvjpw5n/FQ9VL2pvpnlX29kyZz1fPvlWmb/dzFWm4Xx04ZxwswxTJ4+EldPLvrSEj/VQ+v6dcZhb6kMDm3UaIy1i0tZMGsV82etor7Kg9mqMGHqcKaeeyzHnzoKq72LEbxd5ayzYPNm2LgxsfW24ajx/hkc2miaxsblO/j64xXM+2gF9VUe3MkOTjxnHKddchyDR/c98PtgVYX0dH3Y9/TTiel4OxiiMjjk0DSNlQu28OU73zH/05WEQ1EGjMxn5mXFnHT+BFxJ+7mO43ffweTJ8OabcMklie10GwxRGRzS+L1B5ry/lFlvLGLrmnLsTiunXjyZ866bSl5RZvcqe/BBuPNOqKrSZ6j3EIaoDA4bNq4s48MXv2buB8vQYho/mDmGC35yMkPHdDEKfOZM/YHv2nYDyxOGISqDw476Kg8fvDiPj1+dj98bYuwPhnD5L05j1OSB+y4UjUJaGlx7rT5DvQfpSFRGwI7BIUlGbgo/uvNsXl70B6675xx2bKri1xc9zm+uepotq3e2X2jJEvD7D5orvQVDVAaHNE63nQtvOpl/z/8N191zDptWlvHTMx/mgVteYtf2PVZjOMjPp1owhn8GhxV+b5D//Osr3n22hJimceFNJ3PJrTP0ib0zZkB1Naxa1eP9MIZ/BkcMrmQH1/zqTJ6bdw8nnjmONx//gpunP8jSz1fC/Pm9tgptRxiiMjgsycxN5VePXcmDb92CxabwxlX3QTBIYGLPvB2xOxiiMjisGV08mCc+/TVXj3egAb94aCnL5vXc9KSuYIjK4LDHajMzOlROdNhISE/nniv/ybP3vU90jxeD9xaGqAwOf0IhWLAA28xTefyT2znr6hP43zNzuPOSJ2mo8XZePsEYojI47Fn4/PM8EA6zMC8Pm93KLfddyF1PXsPWdRX84py/s3Vtea/2x3Cp9xABX5CasnrqKxtprGqiqc6Lr8FPc5OfYHOIcCBMJBRF0zS0mIYwmVAUE2aLmdz+Wdz01ys7bWPdok189tJcRhw3mOPOPJaUzGTUqIqnzofdZcOV7OyFIz24LFy4kFNOPJGIqmJ1OJg9ezbFxbqzYuvacv7w4+fwNQW4+6lrmHTKyE5q6zpHdJDiwUTTNCpLa9i+difb15azc+MuKjZXsmtrNb5G/175TSaBK9WFM8mOzWHDYjOjmBVMigmp6ev9qZEYkXD76/i1pbHaQ+mqMk696kQ2LillzfyN/ODciQR8IT557it2rCvnkl+fw+Bx/dm2ZifLv1qDO9XF2GkjyC7MpLnJT0yNkZKZ+LXEe5OSr74ioqrEgEgkQklJSauoBo4s4LEPbuMPP36OP93wPHc8fjVTzhzb430yRNUNvPU+Vn+zgXULN7NpaSmbl28j4A227s8uzKRgSB5TLy4mpzCT7MJMMvPTSc9JISUrGWeyI2FLOddW1GN32Rl5/FA2LN5KTNXX80tOd3PuLafx9f++RVH0hTJXlKzFmeygZmcd29eVY7aa+fLVr1n9zQYmn3ksM3980sFZSyIBTLNYsAIRkwmr1cq0PWZTpOek8MCbt/C7q//FX259GTUa46TzxvdonwxRdYCUkm2rd7Lwo6V89+lyNny3FSklFquZAWOKOOXyExg0rh8DRhVSODwfh2s/Y4D2p2+abBVCQ2UTE08b07rP3+RHjagkpbtorPEQi8Y4/pwJbFy8FYvNzLuPz2LsSSO5+Jdn8+ZfP2D9ok0c84Nhvdb3RFI8bx6zMzIoue02pp18cquVaosryc59r/6E3137DA/94lWcbjuTpyduKLgnhqj2QEpJ6codzHlrId+89x27tlYDMHTCAK6453zGTx/F4PEDsHb1Jc49xNAJA/nqzQVsXrGNpDQ3iz5eRm7/bIQQVGytJtgcxu6yYbVb8XsCJKe78db76DMwh6ZaL+nxhXIaazzYnb13MUgoZWXw6acU3303xffc02FWh8vGn168kTsueYIHbnmJv73zUwaPPrD1APeFIao4QX+IL16ex4dPf8GO9RUoZoWxJ43gotvPovis8a0n4aHEFXedR31lEymZSSz7cjVCCGrK6ljw/mLKNuwiPTeFU6+eSjSs8u7jn7J9XTnHnjKKAaML8TU2E/SH0NQYaYfTyrNtef55/Y0p11/fpewOl40/vHADt533CL//0bM8/vHtPbLq7lHv/fPW+3j38Vl88PQX+BqaGTpxIKddM5UTL5hMckbSftcbU2NUllaza2s1VdtrqCmrp7G6iaYaL80ePwFvkJA/TCwaI6bGECaB2WLG6rDgSnbiTHKQkpVMWk4Kmfnp5BRlkTcgm4Khfbo8zJRSIoSgrqKB6rI6YmqM0VOG09zk59U//w9vfTPn//R0Bo/rv9/HedBQVf1NHqNHwyefdKvojo2V/PycRxg2rog/v3bzft1PGkGK7eCt9/H2Qx/xwdOfE/KHKT57PBfffhYjiod0e/ERTdPYvGwbaxdsZPPSUrau3EH5xl27PdE3WxRSs1NIy0nBnebCmeTA7rJjtigoZgVN09/0EQ5GCPpCNHv8eGq9NFZ7CDaHdmsvpyiL/qMKGTK+P0MnDmL01BGHzsqwvcUHH+ir0L77Lpx3XreLf/bWIh791Zv86I6zuPiW6d0ub7jU2yClZO47i3jytpfw1vmYdnExl915Hv1GFnSrnkgowpLPVvLNe4tZPGsFTTUeANLz0hg0th8TTx9L4bB88gfnkts/m/Tc1P32/DU3+anaVsOurdXs3FjB9rXllK7awbcf6wvnW2wWxkwdQfE54znh/MmH5FA14TzzDOTlwZln7lfxUy+ezJI563nl75/ygzPGkN8/K2FdO6osVUNVE4/d8jwLP1zKkPEDuO3pGxg4pqjL5TVNY9XcdXz2YgkL3l9CwBckKc3FxNPHMmnmOMacNJLMPukJ629nBJtDrFu4icWzVvDtJ8so31SJEILRU4cz46qpnHjhcTjch6kToiPKyqB/f7j7brj33v2upqHaw/Un3c+oyYP4479v6FbZjixV/GVjh2YaP368TBQr562TF+TeIM9Mulq+8/ePpBpVu1xWVWPy85dK5FWDfiqnmy6W56ZdKx+6/p9y8WcrZDQSTVgfDwRN02Tp6h3yxd+/Ja8e8jM53XSxPDv5avnMr1+R3gbfwe5eYvnd76QUQspt2w64qneeni1P7/tzuXTuhm6VA5bIfZy3B104HaVEiWref7+VZ7iukj8+5na5Y115t8ou+XylvGHML+V008Xy/026U85+7WsZCoQT0q+eQtM0ufrr9fKBK/8hZyiXyPMzfiTffvgDGQnv3wUgGolKVY0luJf7STQqZX6+lKefnpDqIuGovGLi7+Sdlz7ZrXJHtag+e2muPM12ufz5ib+XnvquX7HrdjXIP1zwkJxuulhePfinsuStBVLTtAPuT2+zdeV2edcZ98vppovlj0b8Qq4oWdut8rFYTN53+WPyz1f8o1vWvcd4/339tH333YRV+dYTX8jT+/5clq6r6HKZo1ZUq79ZL0+zXyF/ffqfZaA52OVypat2yEv7/kSe6bpSvnb//2Q4FDmgfrSHpmnS7w3I+soGuau0StaW10lvg6/HTtxFHy+TVw/+qTzVcqn8+Nkvu1X2rb99IGdYLpPP3f1Gj/StW5x5ppR5eVJGEvc/8TY2y7MH3S7/+bv/drlMR6I6Yr1/3nof91/5BLn9s/jdW7/o8rOdtQs28puzH8TmtPLY/HsZOKZfQvqy+uv1bFqylS0rtlG5tZqasrp2X4BtUkytz6X6jypk8PiBjDx+CAVD+hzQOuOTzxjHqCnDuO/SR3nkpmfw1vu45NfndqnOi395NrtKq3nrbx8w+sThu02J6lXiMyi4+26wJG5GS1Kqi2OnDGXh56u56Q/nH/B67kesqJ7+5Ss01Xj4xzf3djkEonTVDu449T4yCzL4y6y7ye2XfUB9WLdwI2888G6r69ukmCgaUUC/Y/oy6YxjychLw+6yYbFbiUVVwoEInjovNTvrqCyt5ouX5/LBU58BUDSigAtvP4cZV52IYu78jfILFy6kpKSEadOmtc6HcyY5+NN7v+KhH/+T5+9+A8WicNH/nd2lY7n54atZt3AzD13/NC9ueKRX5zm20jKD4rrrEl718aeP5tsv11K6roKB3Xy8shf7MmGHQtrf4V/Nzjp5mv0K+c9fvtzlMrFYTN563N3ywtwbZENV436120Ldrgb5wJWPyeniQvnDzB/J5+9+Ta7+Zr0MBULdqkdVVbl93U75/pOz5I1jb5fTxYXyxjG3y9Vfr+uw3IIFC6TDapUKSIfFIhd8+OFu+2OxmPz9D/8mZzqukBVbKrvcn1Vfr5czLJfJj7o5fEwICXZQ7Enljjp5et+fy49fnd+l/PT0PRVwOrAR2ALc2c5+Afwjvn8VcGxX6t1fUb3w27fkqdbL5a7S6i6X+eS52XK66WL5+ctz96vNFma//rU8J/kqOdN2qXzhnte7dS/XEZqmybnvLJCXFd4kp4sL5SM3Pi1Vtf37r/vvv18qJpMEpALyfpDyuOPkgptvlvf/3//JBQsWyNryenl28tXynrP+0q0+3DzxLnn9mF/1vtPmgw9koh0UbdE0TV4w8g75j7ve6lL+HhUVoABbgQGAFVgJjNgjzxnAp3FxHQd825W691dUNx17h/z1afd1q8ytxXfLmyfccUAnS1OtR57pvFzeOvlOuXPTrv2upyMCzUH5xE+fl9PFhXL261+3m2fBggXS4XBIRVGkw26XC66/Xi4YOlQ64iJzWCxywfz58uU/vi2nmy6W9ZVdt8zvP/WZnGG5rFsXrITQAw6KPbntvEe67FrvSFSJiEybBGyRUpZKKSPAm8C5e+Q5F2gZiy0CUoUQeQloey+klFRsrabfMV18SwSgRlW2rtjBmGkjD+gm9YOnPiMcjPDLF/4fBYO7fngLF8IDD+jbznC47Nz86LX0HdqH/zz8QctFazeKi4uZPXs29957L7O/+oriZ5+l5JpriCiKHiEbjVJy/fUcO1GfTbJ5aWmX+9pvpB4u0RIS0yu0OCh+/OOEOij2JCnFSbMncMD1JMJRkQ+0XTG+HJjchTz5QGUC2t+Nphov4UCYvP5ddzKYFBP/WHAfzv190Vicz18qYexJIyka0fU4nYUL4ZRTIBIBqxVmz4Z24ux276/JxNk3n8ZTv/g321aXMWD03lOtiouLdwvYmzZtGlarlUgkgtVkYtqmTQy/9XL6yYGUrt7B5DOP7VJ/c/vpc+Qqt9V0+RgPmG6GeOwvziQ7O7ce+HElwlK1d2nf8/LZlTx6RiFuFEIsEUIsqa2t7XZnXCkOhBD4Gpq7XMZkMjFobD/6DMztdntt6T+qkNJVZYQC4S6XKSnRBRWL6duSkq6VW//tJpxJDnK6+FK03azX3LkUl5Qgfc08LmcTXfAuDzzwAAu7YCpb1t5ITnN1raMHiqrqojrtND3UoweJRlSstgO3M4kQVTnQ9tJcAOzajzwASCmfkVJOkFJOyMrq/sxhq91KZkE6FVuqul32QLno9nPw1vt47x9dj++ZNk23UIqib7vywoptq3cw9+2FnHHDdFwpXT+5i4uLueuuu3QLdsIJLPzDv3ibJH7y4Sv89p57OOWUUzoVVsuw70AvQF3m00+hogJuvLHHm2r2BHGnHPgKVIkQ1WJgsBCivxDCClwKfLBHng+Aq4XOcYBHSpnwoV8Lg8f1Z/lXa4iEoz3VRLscc8Iwxp86hufvfp0/XvgQNWWdW9riYn3Id++9nQ/9IqEIr977H26dfBeuFCc//MX+hT2APuP+rVe/4yH3ICJCEJOSSChEyVdfdVjuu0+XY3PaKBjaI7fEe/Ovf+khHmed1eNN1e5qJC1r/wNTW9mXB6M7Cd27twndC3hP/LefAD+R37vUn4zvXw1M6Eq9++v9W/z5SjnDcpn84tX2vWM9SSQcka/f/z95pvNyeabzcvncXa/J+sqGA6ozHIrIWf/+Sl496BY5XVwo773kYVmzs+6A6vz42S/ldNPF8tHfPql7CoWQDpALzjpLylj7k2cbazzyDPfV8rFbnz+gtrvMjh1SmkxS3nNPjzfl9wXl6X1/Ll9/7LMu5aenpylJKT8BPtnjt6fbfJbALYloqyuMnz6KvkP78OaD73PiBZOw2q291TQWq4XL7jqfU644gWfveJW3HnyPt//6Hv1GFTLy+GEMGT+AgiF5ZBdmkp6Xhtny/b9A0zR8Dc3UlOkzKrYs38bmZaWsnb+RYHOIAWOKePDz33Ls9NEH1MeVc9fxr1++wqgTh/OzP97MpJnj9NkXW7ZQ/MILcOut8OSTsIcn9K2/fUA0HOXcm089oPa7zAsv9IqDAmh9O+PAkfkHXNcROU1JCMFPHrqKe85+kGfueI1bH/tRr/chuzCLe964jWv+eAmzX/uadQs3MvvVeXz4z892y2e2KNicNtSIutdcQMWsUDSygFOumMIPzp/M+BmjD3he2oL3F3PfZY+RNyCbu175KUKI7z2FUkJmJvz1r2C3w8MPtwpryecr+e+jn3DWjadQNOIAp/F0BVWF557rFQcFwKIv1mCxmTmmo3cKd5EjUlQAE08bwwW/OIP/PvoJwyYNZvoVJxyUfhQM6cM1f7wE0C3Rrq3VVJZWU7OjloaqJiLBCKFAGKvNgs1pw53qIrsok9x+2RQOz0+YlVWjKu88/CEv/vYthkwYyJ8/unPvhW2EgL/8RV/w/5FHdGH9+c9UbqvhwWufomhEATd2YTnqRLDwkUcoqahg2q230tNvnJJSsuCz1Yz7wRCciYiU3te48FBIBxr6EY1E5e2n/EmeZrtcznpxzgHVdbiiaZr8btZyed0x/yenmy6Wf7zoYRnwdTJ1StOkvOkmKUE23nq7vLTo/8kfZl8vd6zvXoDn/rJg3jzpMJn02R8Oh1ywYEGPtrdk7np5et+fyy//812Xy9DDMyoOWcwWM/e+/yvGnnwMD9/wDG88+H67MxC6wppvNvD3G//FrBfm4K33tf7u9wRoqu3917V0hY1LtnLHafdx9xkPEA5G+NN7v+Z3b/9f5+tWCAFPPUXjzPNIfeJhhtTNZcCl6VQ0lvV8p2MxSn72MyKattv66D3Je8+VkJaVxJSzxiWmwn2p7VBIiQqnD4ci8v4rH5czLJfJ31/wsGyoaupW+frKRvnBPz+XaxdulP955CP5zbv6Fa1iS6X876Mfyd+c/Rf5zt/1meAlby+Qj978rFz44RJZXVYrpdTnBFaX1fZKSHpjjUe+9+QsefPEO+V008Xyh1nXyf8+9nG3Ai3VqCrfePB9eabjcvmMs1CfMyhEz1uNWEzKa6+VC+LzExVF6fE2N6zYIU/v+3P52qOzulWOozFIsS1Wm4U7Xvp/DD62P//+7VtcP+ZX/ORvVzL9yilduvGv3VmHM8nOiOOGsHbBRtSovp7fnLcWUDS8gHs/uIO3H/qAbavLKNtQwZevzCM9L5Xhxw2msrSauf9ZxIZFmxk/YzQzrz95N49fIqjeUct3nyzn63e/ZeWctWiaZODYftz8yDWcds00XN14oLl1xXb+/pNn2bxsG1N+OInyAQOIPHDfbs+x2luv/IDRNLjpJnjxRYr/8Admn3rqXvFgiW9S4+nf/5e0rCTO/fHUhNV7VIgK9KlIF952JpNOH8vff/Isf7vuab58/Ruu/ePFDJ80qNPyIr5mX2OVh0kz9WFCU42XsdP0ZYO99c0EfEF++LMz+MG5E5n/3ncIk4mv3viGoRMHcemvz+X1B95l/aLNjJoyfL+PI+ALUra+gq0rtrN5mf4KnR3r9Jea5Q/O49I7z2PqRcXtzgfsiIaqJt5++EPee+IzkjPc/Ob1nzHlgsksWrSIvz36MJFQCKuUTPv4Y/j5z8Ht3u9j2Asp4ZZbdG/fPffA735Hcdwr2ZPM/u9iNizbwf89fDmuA5z32ZajRlQtFA7P5+9zfsdH//qSl/74H35+wu8YP2MUl/76XEafOLxdyzV04iC+emM+m5eVkpKZxMIPl1I0vIC+Q/MI+cOEAmHUiEp6biquFCcDRhfx+v3vEvAG8HuCpOXowmuq8eBMdnTax2WzV+Orb6axponGag+15Q1Uba+hqrSG2vL61nzuVBdDJw7k9B+fxKSZ4+g7tPsh99U7avnPo5/w6fNfoUZUTr1mKtc/cDnJ6bpoWuYMlpSUMK2pieKHHoKpU+H/t3fmcXKU553/vlVdXX13T899SSMJIYGQQCDETWQLG8yCuQL2Yq/tBIckTmLHSRycdZzsOvGxG28uJ47x4qyPGDuObQzmcLjBYIEEktCBbo00M5p7unv67q7j3T+qZ3SguTQjaWZU38/n/bzV3W9XvdVdv/d56633ed7HH3dmOkwXKeGTn4RvfAMeeMCZWjLNxwaToa9ziG/8j0dYcfli1t918vB9p8o5FUzzRPKZAo8/+Cz/8XdPMDyQ5vzLFnPXp27mmtvXvGMoOz2UR7JFBgAAIABJREFUIdk3TKQ6xJbndnDtXVdgWzb/9lc/YbBriNv/4H3EG2P8/BvPoHk9JHqS/M7ffpRnvvsyTUvqWXJJG9//4k+5989up6p+/AiyH2j+bRK9KcBZKC7eWEXDojoa2mppXd7MwgtaWLSylcbF9af03EpKye6N+3nka7/g5Z+8jhCCGz58HR/80/fTfN4Ec/qefBLuuQeqq53tFdNYkkZK+KM/gr//e/jjP4a/+ZszIijTsPjTe77G4b29fP0Xn6G+tXrK+3CDaU5AMV+SP//ms/JjF3xavkf7r/K26t+UX/34N+TrT22ZUqw807Rk174euf2VXfLQzk4ppZTZ4Zz85gP/Jr9637/IA28dmtR+9r55QLbv6JCJvtSMDW7Yti33bz0kv/2XP5IfXf6HznnGf1M++MC/yb6OKU55evNNKRsapIxGpXzuuVOtkJR/8idSgpSf+pTz+gxg27b82n//kbyp9VPyxUffPOX9MM5AxTltqU7Etm22PL+T53/wKq/+bBP5TIFgNMDa913CFe9bzZobLx7tFs0FjLLJjlf3sPGpLWx4/E269/chhOCSd13Iuz54DdfdufbU1wXu6ICbb4a9e9nw2c/yot8/+UEFKZ17py9/GT7xCfinfzojFgrgxw8+z7e++Bh3/+56fvPPJhf05mS4q36cAuVimc3P7eCVRzby+lNbGR5IoyiCJZe0cdE1y1h++Xmcf9kiGpfUz9iSo9Ml2T/Mvs3t7H3jIDs37GHnr/ZSzJXQvB4uXnch19x+OVffumb0Hm/apFJsWL+e9Zs3UxYCr9fLc48+ylU33jj+9/7yL+ELX3BG+77+dThDv99zP9nEVz/9fa6/5RIe+KePTOt/c0U1TWzbZs8bB9n0i61se3kXezYdGJ2nF4j4aVvRStuKFhYsb6ZlaQNNSxqoW1B9WibyWpZNoidJz8F+juzvpXNPN4fe7uLQjk4GjyQAZ+5j24oWLrp2OWves4pL3r3itIUU+/Jf/zWf//znsXCClfwV8GdNTbBy5fHpggvYsGULL/7FX7Du2We56r77nJU7zpCg/vPfX+Mf/vTfWXXVeXzh2/fj9U3PLd9dSmeaKIrCBWvPGx16Nw2Tw28fYe/mgxzYeohDO7v45U83vsPbuKo+SnVTFfGGGLHaCKGqIKGYszaVHvDi1TUUVamsTi+xLRujEv+vmCuRS+VIJ7OkB7Mk+1IM9aYY7EpgmdboMTRdY+EFzVyy7kIWr1rI0ksXcd7qtlPv1k2RdevX4/3Slxw3fY+HdR//OKTTsH07vPCC484MbFAU1ktJWUq8qspzv/EbXHWGBPX4d1/hn//8x1x6/TI+/3/vm7agJsIV1Sng0TwsuXjhccvwSClJD2Xo2tdL9/5e+joG6e8YJNGbItGb4uD2DrLJHMXc5F3tNa+HUFWQSDxEvDHGhVcupa61hvqFNTQsqqNlaSO1rdVndWX544bcT7ynMk3Ytw+2b+fFb3yD8gsvOFOPgBdffpmrrrnmtNbNsmz+31d+zk8efIG161fwuX/52GkXFLjdvzOOaZjOs61ciXLRwLZsbMtGKAJFVdC8HnxBHT2g4/Vp03b1mC1s2LCB9evXOxbN6+W55547rQ93c5ki//uT32Pjczu59aPXcv9f3IFHmziy72Rxu3+zCI/mIRTzEIqdocAps4RxLdoM076rmy//3rc50j7IJ/7qLm796HWn7VgnwxWVyxnjxLBpM41t2/z827/kW1/+OaFIgC8//LusumrpaTveWLiicpkXDPam+PvP/JA3X9rN2ndfyKf/z73Eqs/OM0VXVC5zGsuyefy7r/Cdv3kC27T5vS/+Ov/lw9ec1XtRV1Quc5Y9b3Xwz//9P9i3vZNLr1/G7/313TS1TS646OnEFZXLnGOgJ8X3vvokz/54E7GaMA/800f4tVtXz5qRUldULnOGdDLHj77+LI99+5dIKbnz/nX810/eOKO+UDOBKyqXWU8mleex//cyP33oRYq5Eu++cw0f/vRNp+SycSZwReUyaxnoTvKzb73EUw9voJArcfVNq/jIH7+PhWcq5PQp4orKZdaxf3snjzz0Ei/9fDNSwvW3ruae313PoguaznbVJoUrKpdZQbFQ5pUntvLU9zfw9pvt+AJebv3oddx+369R3xI/29WbEq6oXGYFf3r319i3rZPmRbX81udv4733XDEjy9qcDVxRucwKPvSHN+EP6ay8YsmsGRo/VVxRucwKrrhhGgFkZhmzww/cZU4jpSSTytHXOUSp6DglvvHiLr71xcfYsXHyi3TPF1xL5TImpmGR6E8jFEFVTRiPptKxr5e3frWPob40K69cwmXXL+dX/7mdzS/vRtqSdbddSrw+Sse+XlZdfR77tnVglAxWX7fsbJ/OGWPOi+pn33qJnZsOcvHVS1l5xRJal86eQCxznRcffZM3XtxFU1stF1+9lIuvXkr/kSSvP7sTo2yy7JIFAAwPZlh/5+X4gzod+3o5tKcXr65x+bsuJJcu0LGvl9XXLXPCd83x+yVgwkUu5ryoyiWDPVsP88qTbwEQjgW4cM0ill/axrKLF7B0VeucHUU6m2SH8xQLZT7z9x/mrV/tH224lqxo4b7PvZ98pkjHvj42PL2dWG2YUtGgrqUK07DwB3X6K0FoqmojHGmfeO3jucKet7t56OvPjVtmzovqnk/cwN2/u57ejiF2bDzIjo0H2LnpIK8/u3O0TOPCGpaubGHJihYWr2hm0fIm4vWRedFqni6EolAqGEgJwagfo+wsylBVGx5dbDo1lCWdzLHgvHrefvMQ/qCXwZ4UN37wSl742Zs8/A//ibQl191yibPPOfx7Hzo4wHceeolXXtxNNDZ+Iz1vY1RkUnn2butg/7ZO9m3vZP+OLvo6E6Ofh2MBFi5rZMHSehYsbaBlSR0ti2qpaao6q4FUZgumYfHcTzZR0xRD1zVeefItrrvlEpavXshTD2+g5/Ag5ZLJb33+dgq5Io/83xdRPSpLV7Zy5XsvIjmQYdfmdhoX1MyZmRAno6tjiO/968u88MxO/H4vv37vldz1gSsIhnxu3D9wujTtu3to39XNod3dHN7TS8e+XrLpwmgZj6ZS3xKnvjVOfUuc2uYq6pqqqG6IUtMYI14XmZklLE8zRtkkOZBxwpr1DjPYk6KvK0H/kSR9XQlu+W/X8r57x3dtTw5k+M7fPEFTWw0XrllM5/4+3nfvVezecgjd7yVaFSQ+U4E5ZxkH9vXxw++9ysvP70LTVG6/ey33fOhKIpVbCTeY5jhIKUkOZOg60MeR9kG6Dw3Q15mgt3OI/iNJhoey7/iOL+ClqjZCrCZENB4iEg8SiQUJRf0Eo35CET/+oI9A2IfP70X3a+h+L5rXU0kqiqqiqgKhCIQQlTjcIG2JaVpYhoVRNjHKJqWiQalQppgvU8iVKGRL5DIFsukCuXSBdDJHOpEjncyRGsySGsyQTuZOWu+65jgNrXHec88VXHvzxaf1t51rSCl5a/NhfvT9DWx67QCBgJdb71zDXR9cS9UJ4b5dUU2DYqHMYE+KoUprn+hPk+hPkxrMOBfwUIZMMk86lcMomWe8fooiCMUCRKqCROMhR+jVIeJ1EeJ1UaobotQ2xqhuiBKOBeb0fc3polw2efn5XTzyo43s3d1DrCrIHfdczvvvXENoDF8tN0TZNPD5vbQsrqNlcd2EZctFg+xwnmy6QCFfppAtUsyXKRbKlAplx/KUTCzTxjItLMt2LJQtRy2WUAQej4rqUUYtm7NyvRdfwIs/oOMP6QTDfkJRP/6g7grlFOnvG+aJn23myce2kkrmaF1QzSc/8z7ee/MqdP3Ug266oppBvD6NuC86b+8z5gOWZbN5UztP/GwzG17Zi5SSK65eym2/voZLL1+Moky/gZqWqIQQceDfgTbgEHCPlDJ5knKHgAxgAeZYZtPF5XTR1ZngmSff4plfbGegL00sFuDue6/iljsupaFx/EX4psp0LdVngeeklF8RQny28vqBMcq+S0o5OM3jubhMmnS6wEvPvs2zv9jO2zu6UBTBZVcs5rd//wauvn4Z2gyGgT6W6YrqNmBdZfs7wIuMLSoXl9NOLlfitVf28uJzb/PGawcwTZu2xbV8/BPvZv2NK6mpPLg+nUxXVPVSyh4AKWWPEGKsu3kJPC2EkMCDUspvjrVDIcT9wP0ACxYsmGb1XM4FhlN5Nryyl1de3M3mTe0YhkVtXZjb717L+hsvYsnSU1sb+VSZUFRCiGeBk62u/LkpHOcaKWV3RXTPCCF2SylfPlnBiuC+Cc6Q+hSO4XIO0XMkyYZX9rHhl3vY9lYHtiWpq4/w/rvWcN27lnPBipYZGXQ4FSYUlZTyhrE+E0L0CSEaK1aqEegfYx/dlbxfCPEIsBY4qahcXE5GqWSwbUsHb7x+gE0bDtDZMQTAwkU1fOBDV3PNry3j/OWNs+LxwnS7f48BHwW+UskfPbGAECIIKFLKTGX7vcAXpnlcl3mObUsO7u9jyxvtvLmxne1bOyiXTTSvysWrF3LLHZdxxTXn0TwLg8JMV1RfAX4khLgP6ADuBhBCNAEPSSlvBuqBRyotiAd4WEr5i2ke12WeYVk27fv72f5WB9u3drBtawfDqTwAC9pquOWOS7ls7WJWrV6I7wyshjgdpiUqKeUQsP4k73cDN1e2DwLuJDOX48jnSuze1c3ObZ28vb2Lt7d3kc87rvgNjVHWXrWE1WsWsXpNGzW1kbNc26nhzqhwOe2UyybtB/rZt6eHPbt62L3zCIfbB5AShICFi2pZf+NKVqxq4aJVrdTP8MPYM40rKpcZJZXM0X6gn4P7+zmwv48D+/o4fHAAy7IBCEf8LF/RxPXvuoDlK5q58KJmgnPAlWYqzHlRPfnYFnZu66RtcS0LFtawoK2Guoao62h4GpFSkkrm6Tw8SMfhQQ63D3K4fYBDBwdIJo66nMSrQyxZWs/aq5Zw3vkNnL+skYam2KwYoTudzHlRDQ1meOP1gzz95LbR9zSvSmNTFc0tcZpaqmhsrqKxKUZDY4z6xui0ZiCfK1iWzdBAht6eFD3dKXqOJOnpTnKkM8mRrgTZTHG0rM+vsbCtlsuvXMKiJXUsWlLH4vPqqYqfW4uFjzBv/KnS6QKdhwfpPDxE5+EhjnQmONKZoKc7SekEP6dYVZD6hii19RFq6yLU1oWprglTXRumujpEVXWIQMA7b1vUctkklcgxNJRlaDDD4ECGoYEMA31p+vvTDPQNM9CfGe2ygeO3VVcfoaklTnNLnJYFcVoX1rBgYTW19dGz9qD1bHFOOylKKUkMZenpTtHXk6K3O0V/X5r+vmH6+9IM9KcpVEadjkXXPcSqgsSqgkRjAaIxP5FogHDYRyjiJxTSCYZ8BIM6/oCXYFDH59fw+bzoPu20XmRSSoyyRbFYplgwyOfL5PMlctkS+VyJXLZIJlMkmymSHi4wPJxnOJUnlcyRSuaPszIjeDwKNbVhausi1DVEqauP0tAYpb4xRkNTjPqGKB7P6ZmAOhc5p50UhRCOFaoJc9Gq1pOWyWWLDA5mSQxmGBrMkkxkGRrMMpzKk0zkSCayHDrYT3q4QLFoTOq4Xq8HXfeg6R68mopHU/GojvOhqiooqoIiBAhnBGykbZO2xLYllmVjWTamaWEaFkYllUoGpaLBZNpCVVWIxgJEon4iUT9LljYQjQWIx4PEa0LE46GKhQ4RjQXPOWtzupj3opoMwZCPYMjHwkkswlwum+SyRbKZErmcYw0KBYNCvkShYFAslCkWDcol00llE8MwMcoWZkUktiWxbRvbdpRh2xIhnAZACIGiClTFEZ/qUdA8KpruQdNUdF1D1z3oPg1d1/D5NQIVj+BgSCcY1AmFfYTCPnw+bd52YWczrqimiNfrwRsPvSMQiIvLCO64s4vLDOOKysVlhnFF5eIyw7iicnGZYVxRubjMMK6oXFxmGFdULi4zjCsqF5cZxn346+IyBRLpPK/ubB+3jCsqF5dJ8pNfbuOLD4+/NCm43T8Xl0mz+rxmPvH+q/n+n907bjnXUrmcM5iWTaFUxufV0Dwqezr72Xqgm5WLGrlwYf2E31/cWM3ixuoJy7micpnTlA2TRKaAqgpqo0cnOf/q7UM8v2U/V124kPWrl7JxdwdPv7kXieQ9l57PspZaNuw6jE/zsGX/EQplg8uWtiClnPbMfldULnOWTKHET365jb2dAzTEw6y7+DxWLW5kT2c/B7uHuO3qFew7MsjTb+7B59W4ftVimuIRdnf1078ji0dR+OC7VvPC1v1sb+/hsqUtM1Iv957KZc4S9ut87L2X86X7bmZZSx0He51Q0L3JDNlimZWLGmmuibLzUB9ej4qqKERDPqQtUYQgnS8BUBX2k6lszwSuqFzmPNsO9tCXynD71RcBUBUKkC1UBBPyIwREgz4O9SYolEz6UlnWnN+Kz+vh8dfeZkd7L9esaAOYEadOV1Quc5rOgRQ/fWU7qxY30tGf5M19XSxvraWtvoq/+8nLPLVpN3deu4qm6ig9iTQ/fWUbDfEwDfEwN12+nEy+xKKGOJfOUNcPzoHALy5zh3yxzKG+BAd7EhzoGSLo8/Lx910xZnkpJQ899TpbD3Rz2dIWGuMRhvNFPrjuErKFEnu7BqiJBllQVzXjdT2nA7+4zC5My6YnkaZzIEVHX5JDfUkO9yU51JegL5kdLad5VK68YPxF/4QQ/NbNV570s5Bfn1HrMxVcUbnMKFJKUrkiPUPDHBlMc2RomO7BNF2DwxwZHKZnKI1pH40nGPR5WVhfxZrzW2mrj9PWUMWSxmpaamN45miU4Tkvqp++sp0393ZRXxWiripMXSw0muLhwJz9Y2YjUkqGc0UGhnP0p7L0JzP0p7L0JbP0JjNOSqQplo8PXhoN+miqjrB8QR03XLqU1roYrbUxFtTFqIkE513EpzkvqkQ6z/b2Hp7dksUwreM+E8IZCaqJBomHA8TDfqojQapCfmJhv5MH/USDPqIhP2G/fk6JUEpJrlhmOFdkOFcglSuSyhZIZgokMvnRPJHJM5jOMZTOn/Q3ro4EqY+FWNIY59oVbTTEwzRVR2mMh2mqiRL262fpDM8O82agwrYlqWyBvpTTeg5WWtPBdI6h4TxD6RyJTIFEJkfJsMbcT8ivE/brhANOHvJ7Cfl1ArqXoE8j4PMS1L34fRp+TcOne/BpHnSvB11zktej4tU8aKqCR1XwqCoeVUFVlCkFrJRSYto2liUxLSduoGFZGKZF2bAomxbFsknJcFKhZFAsGxTKJvlimXzJIFcskSs6ebZQJlMokcmXyBRKZPOl47pix6IqgqqQn3gkONoY1USD1EaD1EZD1MaC1MXC1EaDaOdg5NpzYqBCUQTxSIB4JMAFC8afx1UoGSSzeVLZo61zOldkOFcknS+SzpdI54tkC2W6h9LkimXyxTLZQnnMi3AqqIoYDZwpOCFCLU6UWkvak4pCOx5CQFD3EvR7CfqcxiEW9NNaGyMS0J3XIT+RgI9YyDdqtavCAcJ+3Y1Ye4rMG1FNBb+u4dejNFVHp/xdw7TIFcsUysaoZSiWTYqGWbEeTm6YjiUxLHvUyti2xKpEprWlRErpiKgy32zkElYUJyS0qoxEqhVoFWuneVQ0jzpqDb0eFV/FSvq8Gn6vB7/uWFSf5pl39ytzgXNSVNNB86jEQn5i+M92VVxmKefOXbmLyxnCFZWLywzjisrFZYZxReXiMsO4onJxmWGmJSohxN1CiJ1CCFsIcdIHYZVyNwkh9ggh9gshPjudY7q4nA2klHQOD/Po7l38zxefH7fsdIfUdwB3Ag+OVUAIoQL/DLwH6AI2CSEek1K+Pc1ju7icNoaLRbb19fJWXy9be3t5q7eHoUIBAL9nfNlMS1RSyl0wobfkWmC/lPJgpewPgdsAV1Qus4LhYpGdA/3s7O9ne38f2/t6OTw8PPr5kqo469oWcXFDI5c2NnJ+dQ3a739qzP2diYe/zUDnMa+7gDE9z4QQ9wP3AyxYML4/jYvLVJBS0pVOs2twgF0DA+wa7Gdn/wBHMunRMk3hMCvr6rl7xUourm9gZX09EX1qE4InFJUQ4lmg4SQffU5K+egkjnEyMzbmrDYp5TeBb4IzoXYS+3dxeQepYoG9Q0PsGRxkz9DgaJ4tlwHnomyLVbG6sZEPrVrFitp6VtTVEfdPf6bMhKKSUt4wzWN0Aa3HvG4Buqe5TxcXpJT05bIcSCQ5kBxifyLBgUSC/YkEA/ncaLmwV2dZTQ13LL+AZTW1XFhby/nVNQQ07bTU60x0/zYBS4UQi4AjwAeB8ePmurgcQ7JQ4PBwikOpJO3JFO2pJO3JJO2pJHnDGC0X8no5Lx7n+oVtnF9dzdLqas6vrqExFDqjE4unJSohxB3A14Ba4AkhxFYp5Y1CiCbgISnlzVJKUwjx+8B/Airwr1LKndOuucu8oWSadGcydKXTdKWH6UwP05VOcyiVomM4Rbp0NCafIgTN4QiLqmJc3tzMolgVS+JxllTFqQvODi/ieeOk6DI7MW2bwXyOvmyW7kyG3krek81wJJ2mO5M5rqsG4FEUmsNhFkRjLIjGWBiL0haroi0WozUSRZ9gSPtMMK+dFLf0dNOVTlMbDFITCFDtDxD1+VBmQYs1X5FSkjMMEoU8g/mjqT+XZSCXYyCfpy+bpS+XZTCfxz6h4dZVlaZwhMZwmHVtbTRHIrREorREIjSHIzSEQqjK3J3sM+dF9eO3d/KDHduPe08VgpjPT3XAT8znI+bzU1XJYz4fUZ9ORPcR1X1EdJ2IrhPWdcJeL5p67riGW7ZNzjDIlEqkSyUyZScfLhYZLpUYLhZIFoukikWShQKpYpFEIU+iUKBknTwkQbXfT20wSH0wxLIa536mPhSmPhiiMRyiIRSmyuebFd2008Wc7/6lS0V6s1kGcnkG8zkShQJDhTzJgnMBpIpFksUCyUKRVLGAMYE7vK6qhLw6Ia9G0OsloHkJak48iqCm4fNo+DUPPo8HXfWgezzoqoru8eBV1dHkURQ8ioKmOLEpPBVvXkUIVOG0wkKAQJzgTi+REmw54lIvsSqxKkaSYdkYtkXZOppKpkmxkkqWkxcMg4JpkjcM8kaZXNkgbxhkyyVyhjE6vDwWAoj6fMR8PqoqDVLcH6A64KfK56c6EBgV0Ugv4VxplOZ19y+i+4joPs6feNkgpJTkDaPSChdJl4qkj2mls+UymVKJbNkgZ5TJlcvkDYNksUB3JkPeMCiaRiU3x37YdpbxqioBTcPn8eD3aAQqjULc76c1GiXk9RLUvIS83lELHdb1Ucsd9TnbYV13u9GnwJwX1VQQQhD0egl6vTSFw9Pal5TSsRCWSck8ajFGLIhp25QtC8u2MW2JaVvYEmxpY8tKjIpj9nVsd0itBIVRK5ZNEQKPouJRKrEqFOU4i6irjpX0eRzL6Qrh7HJOiWomEUI4XT+PB86tsHYuEzB3h1hcXGYprqhcXGYYV1QuLjOMe0/l4jIFilaZA5m+ccu4onJxOQlSSvqKw+zP9LI/08u+TA/7Mr105AaxJ3iY4orK5ZxGSslgKUN7tp/2bD8Hs30cqKSceXQib6O/iqXhBm5oWMnSSCPv5stj7tMVlcs5gWlbHCkk6cgNcCg3wKHsAO3Zfg7lBsiaxdFyEc3PklA9NzVewpJwPeeFG1gSqiesTd550RWVy7zBtC36isN05YfozA/RlU/QmRukIz9IVz6BJY9OUavWw7QFa7ip6WLagnUsCtWxOFRH3Dt93ytXVC5zBiklGbNITyHJkXyC7kKS7kKCrnxi9PWxwtEVD62BGhaH6llXt4KFoVoWBmtYGKwlMgXLM1VcUbnMGgzbZKCYob80TF9hmL7iML3FJD2FFL2FFL3F1HH3OeB015r8cc6PNPLu+otoDsRpCcRpDdZQq4dRxJl/auSK6hyjZBloijp6sVnSZrCUQQB1Pme9ru58koJVJuTRqffHyJsltiYP4VM1VlctmnL3yLBNEuUcQ6UMQ6UMgyOpmGaglGGglGagOEyinHvHd8MeH/X+GM2BOJfFF9Por6IpUEWTv4pmf5yQ5pv2bzLTzHlRbUse5kghQUwLEvUGiGoBot4AQVWf1z47p0JXfogHtjzMZy68lUuq2rClzcbB/TzVvZWw5uPW5stoCVTzrQPP0+iPkbfK/MH5N/FS/9u0Z/vRFY2sWeL6ugsmPNafbP4enblBhspZ0kbhpGWqvEFq9Qg1epgLIs3U+iLU6hHqfVHq/VHqfTGCnrk3sXLOi+qJ7i080rnxHe+rQiGi+Ql7/EQ0PyHNR9jjI6T5CXl8BD36aB70+AioXgIeHb/qJeDx4le9+FQvujI/ViMsWgY/69zE7S1rMG3HwTBvlnmmdxtfuPgesmaRv931OB9ZdD2tgWo+tmQd3zrwPPsyvbw2uI//ueoeSpbBl3Y+MilRBVSdtlAdl3oXE9dDxL0havQw1XqYWj1MXA+hKXP+8jspc/6s/mDZTdzbdi2pco5hI89wOc+wkSdt5Bk2CmSNAmmjSNoo0J1PkjULZM0SZduc1P4VBLqq4VM1dEVzHBMVDa/iwat40BQPXkVFUzxoiopHqGiKiiocx0RVqI7rhlAQOA6Ko2v9It4ZFVGCjbN0qY2suInYWMck07YwpY0pK64mtsmfX3QXMW9gzPPYkmjn/EgjBcugYDkRiBQhKFvO76AJlbJtkrfKo9YhqOoULQOr4tipCuUdrvFj8YWL75lUufnInBdVyOMj5PGxMFgzpe+VbZOcWSRvlsmZRXJmiYJVJmeWKFoGecvJi1aZgmVQsgyKlkHZNijZjndt2TbImgUM28KwTUzpeOQa0sKqXPgjgjArXrwTPY0/FgXHr0rB8adyxDkiWBVNqBXvYg/GBI3E5kQ7hrTYl+khpgVYW70ETVGp8UUE8EGqAAAMLElEQVQ4kk+QNYu0Bqpp8MV4IreZA5k+jhQS3NJ8GUvCDfyyfzcl22BVzI0aPBFz3p1+LjIirrF++xFrdjp4uuctYt4gT/ds488vupMj+QTfbX8ZXfHwscXriOshftzxGjmzRK0e4ebm1aTKOR7p3IRX8XBH6+UE5uB9zkwznju9KyoXl1NgPFG5rh8uLjOMKyoXlxlmzg9UuLicKQrmMInyYYZKh8ct54rKxeUYbGmRNnpJljtJlrtIljpIlJ1UtNIT7wBXVC7nIFLaZMwBhsvdpMpHSBlHSJW7SJaPMFzuxubo4wm/GqPK28J5oWup0hdQ7V1Ilb6APzzpkm0Orqhc5iUlK0fa6CVt9DJs9JAu9zBsOClt9GLJo0vwqEIj5m0m7l3A4tBVVHlbnaS34FejUz62KyqXOYeUkryVImP0kTUHSBt9ZIx+MkZfZbuPop057jteJUBUayLuXcji0FVEtSai3iZi3mbCnlrEDM5md0XlMqsw7TI5c4icmajkQ2TNQbLmAFmjkpuDx1kaAE34CGv1hLV6GvzLiWiNRLR6olojUW8juhI+Y3M4XVG5nHYMu0jBGiZvJilYKfJmiryVpGCmyFkJ8maSvJkgZyYpnWBhwOmeBT3VhDw11PuXc56njrBWS9hTR0irJaLVn1HRTMScF9Xh7CYGS+341DC6GsanhNDVMLoaQleCeJXAlEx7X2EPrw48RNTbxNLwr9EaWI0QgrTRx8bBf8OUJdZWf5i4voDNQ/9BzkqgKyEur76XgpVi49D3Me0Sa6s/RMQ79s3sXENKiSmLlKwcJTtHycpQtLNOPprSx6WCNUzBSmPK4kn3qQkfAU+cgKeKuL6QlsBqgp44QU91Ja8h5KnGp0ZmjWAmw5wX1f7sq+xIPT5OCYFX8eNVgvjVCPcuenDc/UkkqvBStvOEtbrRP3Nz4j9YW/0hPIrOpqEfsKb6A2TMAdbWfIhNgw+Tt1JsSfyYFdGbUIXG9tTjXFX7GyjizC0tI6WNJQ0saWDKspPbJSxZxpRlDLuIaZcwZRFjNB9JBQy7QNkuULZzlTxf2c5TtnLYnHxNqhF0JYxPjeBXwwQ8car1NvyeGH41ik+NElBj+D1RAmoVAU8MTTl9Lu1nkzkvqnfXf4rrau+naGcqrWaWopWmbI+0qLnRbSnHvygA6n3LuK31ixTMYX7Z/yDrG/8IVXgomClCWi2KUClYw6SNPiJaPX41StTbVLlJ7qFGX4IQgozZP+GxLGnw48OfPu49CUgcVwspbWe9KixsaSOlhY2FLZ0ksbCkiS1NLGmMfm/qOA2PpvjRhA+vEkBT/ES0OrwVa+9Vg+hKEF0J4VWDx/UI/GoErxI8ow3IbGbOi0oIgVcN4FUDoNXPyP4A/J4oZTuPKpyfyKPo2NJEESqq0AioMfJWCoC8mcKvRlCF9+h+HMeNCY+nqyEk8oSyiuNvJVRnUTgUFKEgUFGEihAqKpVceFCFhlLJR7Y9wosqNDyKjkfoeIQXj6KjCq8jHsWHR+h4FT+q8M6p7tVsZ86LaqY5mPkVh3IbKVlZLq66jae7/xfvbXqAS6ru4IW+f0RKyaqq9xP1NmHZZV7tfwhTlohoDayM3cILff+ABC6M3jThvZwqNG5v/cqZOTGXM4br+jEGUtoIoWBJc9RaGXYRicRbuRcw7AKWNBEo6GrQWWDaHMLGIuypc1v/ecy8Xp70dDFiZUYEBaApx0fu0RQ/2nHfEYS0qXkgu8w/XFG5uEwSKUtgHgarfdxy0xKVEOJu4H8AFwBrpZQn7asJIQ4BGcACzLHMpovLTHDiGspT+q6dB6sTrA6wOpBmB1iHHTHZ3TCJGCPTtVQ7gDuB8R/+OLxLSjk4zeO5nGNIWQZpglARwomNIe0sGNtBCSG0lUhZgNJrIIdBbUN4L0Eae5D5hxGeNgh8CHHMyOzJsDP/CIUfgn3CJSpi4GkF76UIz52gLgJPG7ByzH1NS1RSyl2Ae0PuclqQVi8y+48gdIR+A+jXVAT0LNLYiVCiSFkEpQFZegHhXYMsvQSeBVB6DuG/A+whyH8PgveNa8GE2ozU1yHUVlBbnX2oCxHK7J2lLoGnhRASeFBK+c2xCgoh7gfuB1iwwA2Hda4ipQ2llwAboTTBiKWxhpDljSjRLyGtfmT27xCBDyO0CxH+90Pu22DsRlpdKN5LHGGWnp/wiaEI3IXgrhmp+4SiEkI8Cyf1yPqclPLRSR7nGilltxCiDnhGCLFbSvnyyQpWBPdNcIbUJ7l/l3mItHoR+o2OhUp9GuG9HIQGsuwUEDqMzFaXFcdCaYAIwsjsGeFnMvdBM8mEopJS3jDdg0gpuyt5vxDiEWAtcFJRTX3fBcCDENqEZV1OD1LaILNgD4NMV/JhJ7eTSHsYZArsJNhOLoK/jQiMZxmE0xXDcr4nQs5+lAiorcjyRmc/3jWgNiHNH0DhUaTdj9BWIPRrsdNfcfbjv9vZ43xx/RBCBAFFSpmpbL8X+MJM7V9mvgr57yGFH0TYSUoERAiUkJOLEEIJOS3YaAo4rZgIHLM9knwz6rQ223Ae+JdAFkEWQOYr+ch2Huw8yBzIHFJmwc45wpEZsDOVPOuISGYZ1xoIP4goKFWgxEC7ENTxn+cJIZC+9yIzXwJjC0K/Bpn9GkrkzyHwAWT+BwglUhmE8IHvJpAlhP82hPAgfTci1AWgBEFdMqO/30RMa0aFEOIO4GtALZACtkopbxRCNAEPSSlvFkIsBh6pfMUDPCyl/OJk9j+ZGRWy9CoYWyutYbbyh1f+aDtbuRByzoUyJTQQvkrSAa+TC29l2+t0RdAquaeSqyA8lVNVQag4keBGclFpMY9Nx50RYFcu/JFkAXalS2MBZmXbrHR7jGNyAyg7XSRZrmyXjklFoMTUukRapZEKHtNwhSp5GES00mjFnAZNiVZE5AhpZNRuPuFGqAVnhrosVERWaYXt/NGWWZYqwiuCLDrdyuMuxJGLc+RiNY65aI+9sK3KhW1z9OK3nfdHRTIVlKNJqDji9FSEO7KtVV5rFdFXcuEF9KONgdABX8USjzQYx1roEasddF4rjlWfaDj6XMSdpoQz4xsRAkKTK3+a6nG8BRoRmDzhiMdaNJe5xjkjqtnC0a6fy3xl/t6Nu7icJVxRubjMMK6oXFxmGFdULi4zjCsqF5cZxhWVi8sM44rKxWWGcUXl4jLDzOppSkKIAWD8ZeugBpgPHsXz4TzOpXNYKKWsPdkHs1pUk0EI8cZ8iHkxH87DPQcHt/vn4jLDuKJycZlh5oOoxox3MceYD+fhngPz4J7KxWW2MR8slYvLrGLOiUoIERdCPCOE2FfJq8Yod0gIsV0IsVUIcXZWOTgBIcRNQog9Qoj9QojPnuRzIYT4x8rn24QQl56Nek7EJM5jnRBiuPLbbxVC/MXZqOdYCCH+VQjRL4TYMcbn0/sfpJRzKgH/G/hsZfuzwP8ao9whoOZs1/eY+qjAAWAx4AXeAi48oczNwFM4XoxXAq+f7Xqf4nmsAx4/23Ud5xyuBy4Fdozx+bT+hzlnqYDbgO9Utr8D3H4W6zIV1gL7pZQHpZRl4Ic453IstwHflQ6vATEhROOZrugETOY8ZjXSiTmZGKfItP6HuSiqeillD0Alrxuj3EhU3DcrUW/PNs1A5zGvuyrvTbXM2WaydbxKCPGWEOIpIcSKM1O1GWNa/8OsjFExXlTcKexm0lFxzxAnC0xx4tDrZMqcbSZTx80403iyQoibgZ8BS097zWaOaf0Ps1JUcpyouEKIPiFEo5Syp2KST7pitTyNUXFPkS6g9ZjXLUD3KZQ520xYRyll+pjtJ4UQXxdC1Mi5s+rLtP6Hudj9ewz4aGX7o8A74rkLIYJCiPDINk5U3JOO9JxBNgFLhRCLhBNI74M453IsjwEfqYw+XQkMj3R1ZxETnocQokFU4qsJIdbiXGdDZ7ymp870/oezPRJzCiM31cBzwL5KHq+83wQ8WdlejDMq9RawE2cxhdlQ95uBvTijZ5+rvPc7wO9UtgXwz5XPtwNrznadT/E8fr/yu78FvAZcfbbrfEL9fwD0AAaOVbpvJv8Hd0aFi8sMMxe7fy4usxpXVC4uM4wrKheXGcYVlYvLDOOKysVlhnFF5eIyw7iicnGZYVxRubjMMP8frxYmqpYx8fMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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G3WBa/ki+N3RGh3mMnsrAoBuYEoujO8zTS20xMDhhMHqq44Ban49/rlpBldfLaX2LuW7kKMwmE42BAH9d9gWeSIS7J0xiYGYmr61fS43PR5rNzi1jxhKJx3l25XIC0Si3jj2FfHfKkT6dYx5DVAmklARjMfzRaCJFCMRiBGMxAtEowcTnsKoSVlVCqv45osaJxHVnxYgaJ6ZpRONxVG2Pa4ZGXJOomoYmNeJS6k6Kie3XEUL3sDIJgWIS/GH6+UwoLOyw7QUpKTw0eQpCCB6YN4doPI7ZZOLvK5ZzzcmjcFutvLR2NbeNHcfW5mZuHj2WF9asojUc5o0N6xmdl4/NbOa/Gzdy+7jxWJUjv2D1WOa4E5UmJW3hMC2hIC2hEK2hEK3hEK2hMJ5ImLawnryRMN5IpD35o9EDXuQHQhECh8WCTVF0D1uzglVRdD8rRcGimHCYbZhNJiyK7r2rmHQnxT1evCaxR0D7t18mtnFNI9Vm61KbFu+u5IkvlnLliJOxJURRH/DTPyMDq6LQEAhQ6fFQmJJKSXo6/dMzqPF52djYwLfGjUcxmXht/To681qo9npRTIJMh9MQ30E45kX18to1zN6+jaZgkKZgkNZw6KDisCoK6XY76XY7qTY7Be4UhmZlk2KzkWqzkWK14bJacVutuCxW3FYLTosVl9WCw2zBabHgsFiwmJLrfJgMzigu4YziEr713jtcMXwEADZFaReJIgQZDgeeiO5u4YmEcVttiR7xq6m1qZPzenD+XBZV6nHvUqw2spwOcpwusp1Oclwucpwucl0u8txufetyk263H3V/r57kmBeVNxIhGItRnJbG2IICsp1OMh0OMh1OMuwOspwO0u0OMux2HJZj0zmxM5bXVPPRtm1E43EmFhZx75zZ/GH6edw0eiy//OxTNCm5YvgIBmRk4I9GeXxpGU3BIH1TU7ly+Ah++/lCAGYMGoylk97nW+MncO7AQbSEQjSHgjQnbmZbmpv4vLISX3R/r2ubopDndlPgTiHf7aYgJYU+Kan0SUmhT0oKhSmppHSxRz4WMJwUjxN0V3uJSQgiqtp+A2kNhYhLSZbDgRCC5mCQkBrDYtIv9LimsampEVXTGJGT26moOiOsxmgIBNpTnd9Pvd9Hrd9Pnd9Prc9HfcCPqu0bbyPNZqMoNY3C1FT6pqbRNy2V4rR0itPSKUpNPeqGmoaT4gmA7mqvD7H27pEzHPu+lTDL6dznu2IycXJuXtLaYTdb2sVwMOKaRlMwSI3PS7XPR7XXS7XPS5XXS3lrC5/t2kkk/tVSIJMQFKak0i89PZEy6J+RwYCMDApTUvcZvh4NGKIy6HUUk4k8t5s8t5uxBfvvl1LSGNQNK5UeDxVtrexsa2NXWxurNm/CH42257UqCv3TMxiYmcnAjAwGZWYxKDOLARkZ2MxH5vJOylGFEM8BFwENUsqTD7BfAI8DFwBB4BYp5cqv5zMwAL3XzXW5yXW5Gd9n38cJUkqagkF2trWys7WVHa0tlLe2sqGhgdnbt7UbqUxCUJKWzpCsLIZmZzM0K5thOTkUp6V3aow5XJIl5eeBJ4EXD7J/BjA4kSYBTye2BgbdQgihWxldLiYW7vtanIiqsrOtlW3NzWxvaWZLczNbmpuYs2N7u8O902JhSFYWw7JzGJaTy4icHIZm5+C0WCgrK2PBggVMnTqV0tLSQ25jUkQlpVwohOjXQZZZwItSt4osFUKkCyEKpJS1yTi+gQGAzWzmpOwcTsre1ws4FIuxNSGwzU2NbG5q5INtW3l1/TpA79Uym5pZ/cjviMfjWGw2Ppozh7MmTz6kdvTWoLMQ2L3X96rEb/uJSghxB3AHQHFxca80zuD4xmGxMDo/n9H5+e2/SSmp8fnY2NjAhsYGXvnr08RVFQ2IRCNc8fvfMqGinNF5+YzOL2BsfgGDs7Iwd8Eo0luiOtAg9oC2fCnl34G/g25S78lGGZy4CCEoTE2lMDWV6QMHMUkKzvn3y0QBs9XGDTNn4XWnMH9nOW9u3ACAw2xmVF4+Y/IPYF3Zi94SVRWwt99yEVDTS8c2MOiU0gEDmC8lCy64gKk/+Un7nEpKyW6vh1W1tayuq2V1XR3PrVrRYV29Jap3ge8IIV5DN1B4jPmUwVHFihWUAqX33Qd7GSmEEO3P3WadNAzQDSL27/3woFUly6T+KjAVyBZCVAE/JxHsW0r5DPAhujl9O7pJ/dZkHNfAIGksXw5CwNixnWbt7PlXsqx/13ayXwJ3J+NYBgY9wooVMGQIpBy+P9nRtb7DwOBIsWIFjBuXlKoMURkY1NdDdTWMP+D62G5jiMrAYEXCmpeknspYUNvDSClR4wm3+rjuWq9p+nt/D+hOj+5GL4RAUXRvYUUxYVZMR91q7OOGbhgpuoIhqgSaJglEongDYbzBML5gBF8ogj8UJRCOEAzH8IcjhCIxgokUisQIR2OEoyqRmJ6iMZVILE4sHiemxolryXt+LQRYzQoWRcFqMWO1KNjMZmxWMzaLGbvVjMNqwWmz4LBbcNqsOG0W3A4bLrsVt8OK22EjxWEj1Wkn1WkjxWnHrJzgYk2ikQKOY1FJKfEFIzR5AzR5ArT4gjR7g7T4grT6QrT6g7T5Q3gCYdr8IbzBSKcxKmwWpf1Cddit2C1m7FYL2Wk27IkLe8+FbjErWMwK5kQvYzbpW5NJYDLteak2ulL2brem92Capjsd6r2bhhrXiKl6MJloTBdsRFWJJAQdjqqEozG8gbAu+GiMYDhKMNLxu3sB3HYraS47aW4H6S4HGSkOMtwOMlOcZKY6yUpxkpXmIivVSYbbefyJcMUKmDIladUd86JaW17Lhl111LX6aGjzU9/qo8kToNHjJxLbP+a12WQiPXHRpLsdDC7KId1lJ83laL9zpzr1O/meO7vLbsXlsB62V+yRQNMkoWgMfyiSSFF8oQjeYDjRK0fwBPbcXMK0BULsrGuh1R8kHFX3q88kBJmpTnLT3e0pPyOFvIwU8jNTKMhMJTvNdewIL8lGCjgORPXRss28vmA1VrNCboabvPQURvYvIDvNRU6ai+xEykxxkpXqItV57L+ouTuYTEK/Kdit5GV0b3gTisRo9gZo8YXae/w9N6yGNj9VjW0s31qFP7RvXArFJMhNT+GFH19DdpormaeTfJJspIDjQFS3z5jEHRdMIt3tOKHE0hs4bBaKctIpyjm4azxAIBylvtVHXauPuhYfNc1ealu8pLntHZZraPPz9uL1bNndwNljB3Pu+CHto4EVW6uoafYwYWgx+ZkpBMJRojEVu82Cw5rEAD5JNlLAcSCqzFRn55kMehSX3cqAgiwGFBz4FaIHIzfdzfXnnIKUkudmf8n26kyGFefx6ert1DR7CUdVFqzdweWTR/LRl5vYUdtCJKpy0/Rx9M1N56W5K9hYWc/VU8cwbnBR5wc8EEk2UoDxnMrgCCKlxGW3Mm/VNopy0slL1y/sJRt3UTq8hNtmTKS6ycPKbdX4w1G+O+t0hpfkEomp/Gv2Mob2zeVHV05l5Ta9VzskkriSYg+GqAyOGEII3vhsDXaLmVmnjWgfdURjcdwOPQ5gJKoS1zTsFjNmxYTTbiUcU6lsaKVvTho56W4a2vyoca2jQx2YHjBSwHEw/DM4dpm7Yiv/+3wdJ/XNRSDYtLueuy8+nSmjB7JgzQ7S3XbyM1MYVpzHF5sq8QTC7KxtYfSAPjhsFmxW/fJV4xpu+yEE4+wBIwUYojI4gkw7ZTClw0uIxFQ0KemTnYpZMTF5ZH/mLN9KQ1uAS047mQy3g7656by2YLUe3iwjhWvOGss/PviCuKYxdfRA0t2OTo/3/hcbGdwnm0GF2frqlB4wUoARodbgGMYTCBOMRMlNd3e6hMsbCDP13qcB/WH3qAF9+NErfyavoQbT5s1YLd3rX4wItQbHJWkuO2mujs32e0hx2nj/N7exekc1q7fXsGp7NfZ1a/mkYCC/vuevjOzfhwlDixg/pC8n988/rAf9Rk9lcGJSXw/5+Wy750HemTSdFVur2FrdiJTgtFk4ZXARpw4r5tRhJfTPz9zvGajRUxkYfJ2EkWLwxedx75lnAvpwcvnW3Xy5uZKlmyr5fP1OAPIy3JQO68dpI0qYdFIxKc6Oe0dDVAYnJgcwUqS57JwzdjDnjB0MQE2zh7KNFSzdVMG8Vdt4e8l6FJNg9MA+HVZtiMrgxKQLKyn6ZKVx+eRRXD55FGpcY/2uWhav38WiRA92MIw5lcGJSVGR7u7x8suHVLyjOZWxosLgxKOHVlLswRCVwYlHD62k2IMhKoMTjx5aSbEHQ1QGJx494O6xN4aoDE48VqzosfkUGKIyONHYY6ToofkUGKIyONHoYSMFGKLqFkfzMz2DLtLDRgo4gVdURCN6+C2r7as/QSQSY9eORqw2M/0H5qKqcTatryYQiJCdncKgofnU1bYx98O1ZOWkcN4Fo1HMHd+XPG1BGuo9xGJx4qqGqsb1mH5xDanJfV4nKQCEQFEEJsWkR6Y1mzCbFaxWMxaLgtVmxm63YLNbsFrNRrCb7tLDRgo4QUW1ZWMNr764mMwsN9/70QwAVDXO0s+3sWr5TlLTnASDEfLy05nz0VqGnFTAhnW7KSzOZNGnmyjun00sGufD91Yx89KOhxGfzt3AU3/+uEfOQwiwO6w4HFYcTisulw2X24bLbcedYic11UFKqoO0dAdpaU7SM1ykZzjJyHTjcFp7pE1HPStWwNSpPXqIE1JUQ4f34Yf3X8jfnpjb/punLciypTu496GZeNqC/P3JeVx29SQGDspj5qXjePOVMnZsrWNneSNXXleKpy3I356c16moJpYOJCf3SixWBbPZhGJWUNoj1QoEQu+iEl2WHp1WI67qsdfVRO8Wi8aJRlU9RVTC4RjhcJRwMEYoFCUYiBAIRgj4I7Q0N+HzhfF5Q8Si+wcUBbA7LGRmusnKSSEr201ObirZOank5KWSm5dKbl4a6RnO46sn7AUjBZygogIQJoG2V5xzs1khFtOHhBaLgqrGicc1hOmri0oxK2iJACNWmxm6MMfqU5RJn6LMJLe+64TDMbxtQVpbA3jagrS2BGhrDdDaHKC5yUdzs5+tm2pZsnAr0a9FpLXZzOQVpFPQJ52CPhkUFGZQWJRBn6JMCgrTMZuPsYi9vWCkgONAVBvXVbF2dSWVuxqp3NXMxNKB3PTNzuNia3GNcDiGqsbxeUO43HZy89PYsrEGrzfE0GF9yMtP48N3V7F08TYa6rwMvDyPUWNLePXFxcTjGlPOGdELZ3h42O0W7Plp5OandZhPSonXE6Kx3ktDvYf6Og/1tR7qatuorW1j7epKQsFoe35FMdGnKIPikmyK+2XTb0AOJf1z6FuShdV6lF5WvWCkgONAVJ/MXc87/1lOdk4Kxf2yycrufALa2hLguWc+oaHey1tvLKOuto3v3nM+My8dx1tvLMPptHL5NZNwumyMmzgAnzfE6VOGYrWZOWv6CFav2IXdbmHU2JJeOMPeQQhBWrqTtHQng4bm77dfSklba5Ca6haqd7ewu7KZ3RXNVO5qomzxVrS43mubFEHf4iz6D8xl4KA8Bg7JZ9CQPDIy3b19SvvTC0YKOA5cP1pbAlitCq5OQgwb9ByxWJyqymZ2lTeyc0cDO8sbKN9WT0O9tz1PZrabIUMLGDKsgJOGF3LS8D6kpHYeASmpFBXpRop///uwqzqu3ekzMo/yAPgnABaLQv+BufQfmMtZ078aEvu8Icq317N9az3bttSydXMtXyzZ1j4V7VuSxYiRRQwfWcTJo4opKt4/FkTS6CUjBRwHojI4eklJdTD6lH6MPqVf+2+BQIQtm2rYtL6aTeurWLxwK7PfXwNAWrqTk0f3ZdSYYkaNKWHA4DxMpiSJrJeMFGCIyqCXcblsnDK+P6eM7w/oc7XdFc2sX7ub9WsqWbdmN4s/2wJAapqDMeP6MW5Cf8ZNHEBeQcdvH+mQXjJSgCEqgyOMEILifroF8YKL9Qu+od7D2lWVrFy+k1XLdrLwk00AFBVnMn7SQCacOpDRp5Rgs3XjlTq9ZKSAJBkqhBDnA48DCvCslPK3X9s/FXgH2BMx439Syl91Vq8Ro8JASkllRTMrvjuDyXkAACAASURBVChn+Zc7WLOigmhUxWYzM3Z8f0rPGEzp5CGdWxeTaKSAHjZUCCEU4ClgOlAFLBNCvCul3Pi1rIuklBcd7vEMTiyEEJT0y6akXzaXXT2RSCTG2lWVfLlkO0sXb2Xp4m089vsPGT6yiMlThzF56kn7P5PrRSMFJGf4NxHYLqUsBxBCvAbMAr4uKgODw8ZmszDhVH0I+O0fnsvOHQ0s/mwLn3+2mWf+Mpdn/jKXk4b34cyzhzPl7GG6wHrRSAFJGP4JIa4AzpdSfjPx/UZgkpTyO3vlmQr8F70nqwHulVJuOEh9dwB3ABQXF4+rqKg4rPYZnDhUV7Ww6NPNLPx0E9s21wIwckwxd7aVMfi1vyE8nqTNqXr6OdWBbJ5fV+pKoERK6RdCXAC8DQw+UGVSyr8Dfwd9TpWE9hmcIBQWZXLNjadxzY2nUVPVwqdzNzDv43U0zVmAw57NS4/O49wLRjF2fH8UpedcCZPRU5UCv5BSnpf4/gCAlPKRDsrsAsZLKZs6qtswVBgcLlJK1II+7OgzjAdzLsDnC5OTm8KMmWOZcfEYsnNSD6neng6muQwYLIToL4SwAtcA736tAfki8ahcCDExcdzmJBzbwKBDREMDlvo6TrpxJq+99wN+8pvLKOmfw0vPLeT6y57glw/+h1XLdybVq/uwh39SSlUI8R3gY3ST+nNSyg1CiDsT+58BrgDuEkKoQAi4Rh7Niw57ECnlVx7AcU1fsrPnT9Hu9atgtpgwdfIiM4MusJeRwmo1M+Xs4Uw5ezi11a188M4qPnpvFZ8v2ExJ/2xmXT6BaTNG4nAcngPnMb+gtreJRlRaG720Nfloa/LjafHjbQngawvg94Twe4IEfGGC/jAhf4RwMEokHCUcihKLqqgHcRo8EIrZhMVqxmq3YHdYsTksOFx2HC4brlQH7jQH7lQH7nQnaRkuUjPdpGe5Sc92k5GbhtNtO76cDA+BsttvZ8GzzzJ17lxKp03bb380ovLZJxt5681lbNtcS0qqg1lXjGfW5eNJzzj4utKOhn+GqPZCSklro4+6ymbqdjfTUN1KQ1ULjbVtNNW20VznwdcWPGBZs0UhJd2JK9WBK8WuX/xuGw6nDZvDgtVuwWqzYLGaMVsT3r8JD2AhBFJKpNT9vOJxjXgsTiyqEouqRMIxIqEo4WCUcDBC0Bch6A/j94bwtQWJhKIHbJPNYSU7P42s/DRyCtLJKcwgtzCT/L6Z5PXNIrcwA7PlGHM07AZlZWWcc8YZRDUNq8PB/PnzKS0tPWBeKSUb1lXx5stlLFm0FZvNzPkzx3DltacecHnUcb1K/VCIq3Gqyhup3FpH5fY6KrfVU1XeQM3ORsLBfS/QtCw3OQXp5PfNYsSEAWTlpZGZm0p6dgrpOSmkZ7pIyXDhcB25XiEajuFrC+JtDdDW5KO10UdLo5fWBi9NdR6a6zys+2IHTXWeds9lAJNiIr9vJoUDcikenEffQXmUDMmnZEgBDtchvO39KGPB7NlENY04EI1GWbBgwUFFJYTg5FF9OXlUXyp2NfHmy2W8/9ZK3n9rJdMvGMUNt5zR5bWHx72oQoEIO9ZXsX19FeUbq9mxsZrKbXXtwzAhBHlFmRQNymXkpIH06ZdDfnEW+X0zyS3KxH6Y4+vewGq3kJXokToirsZpqvNQX9VCXWUztRVNVJc3UlXewOrFW4lFvnKnz++bxYARhQwY3oeBI4oYPLJvp/UfbUwFrEDUZMJqtTK1iwFfSvplc+9DM7npm2fy5stL+eCdlcz7aC0zLh7L9bec0akj7HE1/NM0jYotdWxYXs6WVRVsWV1J1Y6GdstOerabAcMLGTCskJKh+fQbWkDRoLxjQjg9TTyuUVfZTMXWWiq21LFzUw3lm6qp2dnU/vfLyEll6JhihowpZvi4/gwdW3J0/+1mzaKsrIwFP/gBU88666C9VGc01Ht45YXFzH5vNWaziUuunMjtd59z/M6pKrbUsmLhZtaWbWfDsp34PfqcJy3LzdDRxQwZXcygkX0ZPLKIzLxj6057NBAKRNixoZrt63azbe1utq7Vb1SgzyMHj+rLqFMHMbJ0ECPG98fuPEqGjV4v5ObCnXfCY48lpcqaqhZefHYhn8xdz9wlPz1+RfX4j19j9mtLKeyfw8hJAxkxcQAjJgwgvzjrhLd89RS+tiCbVuxk/ZflrP9yB1vXVBJXNcwWhWHj+jH2jKGcMuUkBp1c1KMrFzrklVfg+uvh88/h9NOTWvX2LXUMPqng+BVV/e5mFItCdv5hOLAZHBahQISNy8tZvXgbqz/fyo4N1UgpSc10MeGs4ZSeezLjppzUu73YpZfCl1/C7t3QA8/7DJO6Qa/S1uxn1aItLP90E19+shG/J4jVZmHc1JM4Y8ZoJk0bgasng774fJCTA3fcAX/5S48cwjCpG/Qq6VluzrpkHGddMg41FmfDsnKWzF7L4tlrKft4HWarwvgpw5gy6xROO3ckVns3PHi7wgcfQCQCV16Z3Hq7iNFTGfQamqaxZVUFiz5YzcL3V9Nc58Gd6uDMi8dy3tWnMnhU3+TMgy+/HMrKoKqqR4Z+YAz/DI5CNE1jzZLtzHvzSxZ/tIZIOMaAEYXMuLaUsy4djyvlEOM4+v360O+22+DJJ5Pb6L0wRGVwVBPwhvj0nRXMfnUpO9ZXYXdaOfeqSVxy2xQKSrK7V9kbb8DVV8OCBTCl8/Dfh4ohKoNjhi1rKnnv+UV89u5KtLjG6TNGc/mdZzN0dHHXKrjySli0SI9JofTcukZDVAbHHM11Ht59fiEf/HsxAW+YMacP4bofnMfISQMPXigQ0Id+t94KTz3Vo+3raSdFA4Okk5Wfxq33z+TFpb/gtocupmJrHT++8gl+cuMzbF+3+8CFPvoIQiG44orebezXMHoqg2OCSDjKey98zhtPzcPXFuTMmWO5+UcX0qffXnOuPXOpmpoeHfqB0VMZHAfY7Fau+NbZ/Ovzn3LNd6fzxdz1fGvaI7zwhw8Ih6IQDML778Nll/W4oDrDePhrcEzhSnVw848u5MIbT+dfj7zPa0/MZcHbK3no3FQGBYNHfOgHRk9lcIySnZ/Ojx6/gd+9fjcWm0LV7/9K0J6Cd9QBR2S9iiEqg2OaUaWDefJ/3+V0tZKFln7cNeOPrFy45Yi2yRCVwTGP9dN5WKJhRv3pAVypDh664Wn+8Zt3iH3txeC9hSEqg2Of//wHsrLoc8uVPPHhPVx00xn87++fcv/VT9HS4O28fJIxRGVwbBMOw3vv6f5TZjM2u5W7f3MFDzx1Mzs2VvODi//Ejg1Vvdokw/rXQwR9IRoqm2mubaW1ro22Ji++lgD+tgAhf5hIMEI0HEPTNLS4hjCZUBQTZouZ/P45fOv3N3R6jI1Lt/LxC58x/NTBnHrhKaRlp6LGVDxNPuwuG65UZy+c6RHm4491/6mvuXmcOXMshQNy+MU3nuWey/7Cg3+9mYnnjDhIJcnFENVhoGkateUN7Nqwm10bqti9pYbqbbXU7KjH1xrYL7/JJHClu3Cm2LE5bFhsZhSzgkkxITU93p8ajRONHDiO39601nsoX1vJuTeeyZbl5axfvIXTZ00g6Avz4bOfULGxiqt/fDGDx/Zn5/rdrPpkPe50F2OmDie3OBt/W4C4Gict+9BiiR81/Oc/kJkJZ521366BI4p4/N0f8otvPMuvbv8n9z1xE5MvHNPjTTJE1Q28zT7Wfb6ZjWXb2LqinG2rdhL0htr35xZnUzSkgClXlZJXnE1ucTbZhZlk5qWRlpOKM9WRtFDOjdXN2F12Rpw2lM3LdhBX9Xh+qZluZt19Hov+9wVK4iHo6gUbcKY6aNjdxK6NVZitZub9exHrPt/MpAtPYcY3zjpysSQOh0gE3n1XfzZlObCjY2ZeGo+8djc/u+lv/PY7L6LG4px1Sc++p8oQVQdIKdm5bjdl76/gy49WsfnLHUgpsVjNDBhdwjnXncGgsf0YMLKY4mGFOFyH6AN0KG3TZLsQWmrbmHDe6PZ9gbYAalQlJdNFa4OHeCzOaRePZ8uyHVhsZt56YjZjzhrBVffO5LXfv8umpVs5+fSTeq3tSWPOHD1qUicevq4UO7/595387Ja/8+gP/o3TbWfStJ4bChqi+hpSSsrXVPDp62V8/vaX1OyoB2Do+AFc/9CljJs2ksHjBmDtzkuce4Ch4wfyyWtL2LZ6JykZbpZ+sJL8/rkIIajeUU/IH8HusmG1Wwl4gqRmuvE2++gzMI+2Ri+ZiUA5rQ0e7M7euxkklTffhIwMOOecTrM6XDZ+9fwd3Hf1kzxy9wv84c3vMnhU3x5pliGqBKFAmLkvLuS9Z+ZSsakaxaww5qzhXHnPRZReNK79IjyauP6BS2iubSMtO4WV89YhhKChsokl7yyjcnMNmflpnHvTFGIRlbee+IhdG6s45ZyRDBhVjK/VTygQRlPjZBxjkWeBr4Z+l1560KHf13G4bPziudv54SV/5ue3/oMnPrinR6LunvCr1L3NPt56YjbvPjMXX4ufoRMGct7NUzjz8kmkZh36qyzjapza8npqdtRTt6uBhspmWuvbaGvw4vcECHpDhAMR4rE4cTWOMAnMFjNWhwVXqhNnioO0nFQy8tLILswkrySHggG5FA3t0+VhppQSIQRN1S3UVzYRV+OMmjwMf1uAf//f//A2+7n0u+czeGz/Qz7PI8YHH8BFF+nbCy7oVtGKLbV8/+I/c9LYEv7v5bsOaT5pOCkeAG+zjzcefZ93n5lDOBChdOY4rrrnIoaXDul28BFN09i2cicblmxh24pydqypoGpLzT5P9M0WhfTcNDLy0nBnuHCmOLC77JgtCopZQdP0N31EQlFCvjB+TwBPo5fWeg8hf3if4+WV5NB/ZDFDxvVn6IRBjJoy/OiJDNtb3HILvP02NDSAtfuhpz9+fSmP/eg1br3vIq66e/9X7HSGEaJsL6SUfPbmUp764Qt4m3xMvaqUa++/hH4jirpVTzQcZfnHa/j87WUsm72atgYPAJkFGQwa048J54+h+KRCCgfnk98/l8z89EO2/PnbAtTtbKBmRz27t1Sza0MV5Wsr+OKDlbrhxGZh9JThlF48jjMunXRUDlWTSjQK77wDs2YdkqAAzr1qEss/3cRLf/qI0y8YTWH/nKQ174TqqVrq2nj87n9S9t4KhowbwA+fuZ2Bo0u6XF7TNNZ+tpGPn1/AkneWE/SFSMlwMeH8MUycMZbRZ40gu09m0trbGSF/mI1lW1k2ezVffLiSqq21CCEYNWUY02+cwplXnIrDfYwaITrio4/0Id977+lDwEOkpd7DN896mJGTBvHLf93erbId9VSJl40dnWncuHEyWaxZuFFenn+7vDDlJvnmn96XakztcllVjcs5LyyQNw76rpxmukrOyrhFPvrNp+Wyj1fLWDSWtDYeDpqmyfJ1FfL5n78ubxryPTnNdJWcmXqT/PuPX5LeFt+Rbl5yufVWKVNTpQyHD7uqN5+ZL8/v+3254rPN3SoHLJcHuW6PuHA6SskS1cL/fiEvcN0ov3HyPbJiY1W3yi6fs0bePvpeOc10lfz2xPvl/JcXyXAwkpR29RSapsl1izbJR274i5yuXC0vzbpVvvHHd2U0cmg3gFg0JlU1nuRWHiLRqJQZGVLeeGNyqovE5PUTfibvv+apbpU7oUX18QufyfNs18nvn/lz6Wnu+h27qaZF/uLyR+U001XypsHflQteXyI1TTvs9vQ2O9bskg9c8LCcZrpK3jr8B3L1gg3dKh+Px+Vvrntc/t/1f+lW795jzJ6tX7bvvJO0Kl9/cq48v+/3ZfnG6i6XOWFFte7zTfI8+/Xyx+f/nwz6Q10uV762Ql7T9055oesG+fLD/5ORcPSw2nEgNE2TAW9QNte2yJryOtlY1SS9Lb4eu3CXfrBS3jT4u/JcyzXyg3/M61bZ1//wrpxuuVY+++CrPdK2bnHbbVKmpEgZ6vr/szO8rX45c9A98umf/bfLZToS1XFr/fM2+3j4hifJ75/Dz17/QZef7WxYsoWfzPwdNqeVxxf/moGj+yWlLesWbWLr8h1sX72T2h31NFQ2HfAF2CbF1P5cqv/IYgaPG8iI04ZQNKTPYcUZn3TBWEZOPonfXPMYf/7W3/E2+7j6x7O6VOdV986kprye1//wLqPOHLbPkqjepGzRIha88gpTJ0+m1J48A0xKuotTJg+lbM46vvWLSw87nvtxa/37/a1/ZcEbZfzl818zaGy/LpUpX1vB9077CdlFWfx29oPk98s9pGPvYWPZFl595K1207dJMVEyvIiiIQXkFueQVZCB3WXDYrcSj6lEglE8TV4adjdRW15P+ZqK9mdUJcOLuOKei5l+45ko5kOPFqTGVB79xtPMf+Vz7vjDDVz5/2Z2qVwkFOW7p/0UT5OX5zf/uVfXOULiTfNTphCNxbBarczv4KXYh8KcN77gz/e+ypMf3cvALjxeOeGsfw27m+R59uvl0/e+2OUy8XhcfufUB+UV+bfLlrrWQzruHppqWuQjNzwup4kr5GXZt8p/PviyXPf5JhkOds9apaqq3LVxt3znqdnyjjH3yGniCnnH6HvkukUbD6t98Xhc/vyyP8gZjutl9fbaLpdbu2iTnG65Vr7fzeFjMnj4uuukAhKQiqLIhx9+OKn111Y0yfP7fl9+8O/FXcpPT8+pgPOBLcB24P4D7BfAXxL71wKndKXeQxXVcz99XZ5rvU7WlNd3ucyHz86X00xXyTkvfnZIx9zD/FcWyYtTb5QzbNfI5x56pVtzuY7QNE1+9uYSeW3xt+Q0cYX88x3PSFU99PlXY1WznJl6k3zoot92qw13TXhAfnP0j3rXaDN7tlyiKNJhMklFUaTD4ZBLlixJ6iE0TZOXj7hP/uWB17uUv0dFBSjADmAAYAXWAMO/lucC4KOEuE4FvuhK3Ycqqm+dcp/88Xm/6VaZ75Q+KO8af99hXSxtjR55ofM6+Z1J98vdW2sOuZ6OCPpD8snv/lNOE1fI+a8s6lbZJUuWyIcffrj9gnzxl2/I8eJs+ZMHftrli/Sdv34sp1uu7dYN67BYtEhKh0PKMWPkko8/3qf9yeaHl/y5y6b1jkSVDEPFRGC7lLI8MdZ8DZgFbNwrzyzgxURjlgoh0oUQBVLK2iQcfx+klFTvqGf0WV33l1FjKjtWVzDr7vMOa5L67l8/JhKKcu9z36ZocEGXy5WV6dGKp06FzqYJDpedux67hRVz1/CfP77LWdecftA2l735Jgs+/ZSpQ4eC3885v/wlUVXFajYz/+abyaxqZK38lFWPfMIfH/0t83/1K0qnT4eiIsq2b2fBwoVMnTp1n7lLvxG6u0TNjnoK+h/enLNTVq2CCy+Evn3h448pzc2l9Nxze+xwKWnOpASKSYaoCoG9I8ZXAZO6kKcQSLqo2hq8RIKRbv3DTYqJvyz5Dc5DfdFYgjkvLGDMWSMoGd51P52yMt0dKBrVl7HNn9+5sEwmEzPvOo+//uBf7FxXyYBR+y+1Kisr45yrryYqJVbgZiAKxIFoLMaCZ59FCkEc+dVvDzxA6QMPUAack8hvNZuZ/+yzlN50EwhBfj99jVztzoYun+MhsWULnHcepKfDvHmQ28MCBpwpdnbvOPzzSoYP9YFuk183KXYlj55RiDuEEMuFEMsbGxu73RhXmgMhBL4Wf5fLmEwmBo3pR5+B+d0+3t70H1lM+dpKwsFIl8ssWKALKh7XtwsWdK3cpi+24kxxkHeQl6ItWLCAqBC6YEwmuPJKrHY7iqJgdTiYunAhw195G4mCyWTCarcz9bnn4K23WDBz5ldlVZUFt9wCgwfD/fcTWbyUNq2Rdxf8h7Kysi6fZ7eorITp00EImDtX76l6gVhUxWo7/H4mGaKqAvY+6yKg5hDyACCl/LuUcryUcnxOTvdXDlvtVrKLMqneXtftsofLlfdcjLfZx9t/+bDLZaZO1XsoRdG3U6d2Xmbnugo+e6OMC26fhivNdZB6p2K12XQR2Wzc9MMfMv+TT/j1r3/N/PnzKZ08mVQtk1PEFP7fd+5h/iefUHrrrXDJJUx94IGvBGi3M/W++2DgQHj0Uaqum8m6+Dyee+VvnHP22ckXVn09TJumu8nPmQNDhiS3/g7we0K405IQgepgk62uJvQhZDnQn68MFSO+ludC9jVUfNmVug/VUPHzy/8oryq6s0dWQnSEpmnyvvN+LaeJK+QvLv+DrK9o6FK5JUukfPhhfdsRkVBEvvSrN+UFjmvlpVm3yIbdTZ3Uu+SgE/t4PC6/U/qgvLLg9gMuCj5g2aYmeUu/sdK0x7QN8uGTT+684V2lpUXK0aOldDqlXNw103Yy+cbkX8vffOu5LuWlF0zqFwBb0a2ADyV+uxO4U35lUn8qsX8dML4r9R6qqJbNWSOnW66Vc//dPetYMohGovKVh/8nL3ReJy90XieffeBl2Vzbclh1RsJROftfn8ibBt0tp4kr5K+v/mOnguqMD/4xT3+E8MKCLpdpbfDIUscMaTFbdNO22SyXuN36ZVRaKuWbb0p5qGZ+v1+vw2qVcs6cQ6vjMAj4QvL8vt+Xrzz+cZfydySqpCxTklJ+CHz4td+e2euzBO5OxrG6wrhpI+k7tA+v/e4dzrx8Ilb7oTmyHQoWq4VrH7iUc64/g3/c929e/93bvPH7t+k3spgRp53EkHEDEisqssksyMBs+epfoGkavhY/DZX6iortq3aybWU5GxZvIeQPM2B0Cb+b81NOmTbqsNq45rON/O3elxh55jCm3Xhml8u9/od3cavpvPbCm2yp2KhbBkeOhH/9Cx57TI9q1L8//OAHlA0fzoJly/azHh6QSESPNfHFF3owl+nTD+v8DoU9b2ccOKLwsOs6bpcpLft4DQ/N/B0X3zWd7zx+a5Jb1nWqttYw/+VFbCzbwuYvthP0hfbZb7Yo2Jw21Ki631pAxaxQMqKI4acO4fRLJzFu+qjDXpe25J1l/ObaxykYkMtvZz9ETlFWl8otn7OGBy/6HRfdcQ7fe/K2/TPE47o37p/+RNnixftaD7/5TV1YffpAYaGeUlJACH093113MXXDBkr/9S/dTf4I8PdfvcX7Ly3mtVW/wdkFx84T0p1+wnmjufwHF/Dfxz7kpImDmXb9GUekHUVD+nDzL68G9J6oZkc9teX1NFQ00lLXRjQUJRyMYLVZsDltuNNd5JZkk98vl+JhhUnrZdWYypt/fI/nf/o6Q8YP5P/ev7/LgW1qy+v53S1/pWR4EXccLBy1ouhvMbzsMhZ8+9tEn376K+vhM89Q+swz++Z3uSjLzOScqird7G+xMH/oUJK3mq/rSClZ8vE6xp4+pEuC6ozjVlQAt/3fNWxbuZNHb3uauKpy3s1Tj2h7TCYTRYMLuvVg+HCRUrJ8zhr+du9LVGysYvLlk/jRc9/uspt9xcYq7r/gEbS4xk9f+36XAsxMvfFGrM8/TzQaxWq1MvWDD3SzeHW1/j7exHbBvHlEd+/WxadpLEjyItmusnLRFup3t3Dj/5uRnAoPNtk6GlIynBSD/pC8b8bDcrrlWvnKb98+5GVI6xZtkn+8/Rn50T8/kZ4mb/vv/raAbG3wHHY7e4LNy7bLH03/lZxmukreMPA7csm7y7tVfv3izfKyvNvlVUV3yvK1Fd0q25Hlce88Doejx9bzdZWf3Pi0vPaUn8hIuOue0ZyoTop7iISj8uEbnpDTLdfKn1/+R9lS19at8s21rfLdp+fIDWVb5H/+/L78/K0vpZRSVm+vlf997H35k5m/lW/+6T0ppZQL3lgiH7vrH7LsveWyvrJRSqmvCayvbOwVl/TWBo98+6nZ8q4J98tppqvkZTm3yf8+/kG3Hi+oMVW++rt35AznDfKWYT+UNTvqeqy9XRFfT7J5dYU8v+/35cuPze5WuY5EdVwP//ZgtVm474VvM/iU/vzrp6/zzdE/4s4/3MC0GyZ3aeLfuLsJZ4qd4acOYcOSLagxPZ7fp68voWRYEb9+9z7eePRddq6rpHJzNfNeWkhmQTrDTh1MbXk9n/1nKZuXbmPc9FHM+ObZ+1j8kkF9RSNffriKRW99wZpPN6BpkoFj+nHXn2/mvJun4urGA80dq3fxpzv/wbaVO5l82US+/9RthxVUtDNKS0uPyJAP9DnuMz//Lxk5Kcz6xpSk1XtCiAr0+cwVP7yQieeP4U93/oM/3PYM8175nFt+eRXDJg7qtLxIxOxrrfMwccZYQF9nOGaqHjbY2+wn6Atx2fcu4PRZE1j89pcIk4lPXv2coRMGcc2PZ/HKI2+xaek2Rk4edsjnEfSFqNxUzY7Vu9i2Un+FTsVG/aVmhYMLuOb+S5hyZekB1wN2REtdG2/88T3efvJjUrPc/OSV7zH58kmHbW08mpn/32VsXlnB//vjdbgOc93n3pwwotpD8bBC/vTpz3j/b/N44Zf/4ftn/Ixx00dyzY9nMerMYQe8iIZOGMQnry5m28py0rJTKHtvBSXDiug7tIBwIEI4GEGNqmTmp+NKczJgVAmvPPwWQW+QgCdERp4uvLYGD85UR6dtXDl/Hb5mP60NbbTWe2isaqFuVwN15Q00VjW353Onuxg6YSDnf+MsJs4YS9+h3Xe5r69o5D+PfchH//wENapy7s1T+OYj15Ga6e5WPcca9bubeeYXb/H/23vz6DiOO8/zE5mVlXVXoXCDAAmSokiREiVSFHXLsiTrWt1qqb2S1+5dT2vGfbjHO+O2Z+2et+MZu90zvdOH2z3PHrnHttqyu9uybLUOty7rtGRSoihSFEnxAAmAuFFVqLsqj9g/sgCSEkECBEgCYHzeixdZVVGZkVX5jV9kZPx+seaSZVx/7+yuaH/WiQo8q3XH527khk9dzZPfeZ5/+oun+OIn/gvnXryMe//oVq68a8NHhrIf/Mo9pAfHiNVH9Yk7ZwAAIABJREFUeOeF96hWLG78zLX8/X9+jOd++DJ3/eEt6IbO977yYwy/j0giRKIpTuuyZjJDWTLDWaRkStFj/+zTf0NqIFOrqyDZWkfL0iYuvHY1HasWseS8dpZe0EHrsuaTsiRSSnZt2svj3/olrzz2G4QQ3PCpq/nkH9/BonNmNql4PmBbDn/2+UcA+OJfPjhra4aNs2Af/k6HSqnKc3//Ko/9xVMc2jtAKBbk6rs3cvW9l7LuuvMx/FNrexzHZaBriPRghmhdhCWr2ylkizz6jcfJjuS4+/O3TKlbtmfLfgzTIN4YI1YfnZUF2aSU7N/WzWuPb+JX//Br+vYNEooGufV3r+Ou37+Zpo6pPQSe70gp+fZXf8pTj7zOl//m03zsjvUntR+1QMEUcV2Xd17cwYs/fp3Xf76ZYq5EOB5i4y0Xcekt69hw04XzqltkVW3ee303m555hzeefJu+vYMIIbjo46v5+Cev5Op7Np4d6wIfwU+/8yLf+/oT3Pe56/m//sPUgt4cCyWqk6BarrLlhfd47fFN/OaZrYwNZ9E0wfKLOjn/ypWsuuQczr14Ka3Lm2e9+3CypIfG2LOliw/e2s+ON3az49cfUC5UMPw+Lrx2NVfedQlX3L5h4h7vbOOFxzbz51/4EdfcdhFf+ptPz+h/U6KaIa7rsvut/Wz+5Va2vbKT3Zv3TczTC8WCdK7poHNNO4tXLaJ9RQtty1toWlx/SibyOo5Lqj9N//4hDu0doGd3Hwfe7+XAez2MHEoBIISgc00751+1ig2fWMtF16057SHF5hr/8g9v8ld//A+svfwcvvb9h/AHZrYS5lk592820TSN8zaeMzH0bls2B98/xAdb9rNv6wEO7Ojl1Z9t+oi3cV1znPq2OpItCRKNMSJ1YSIJb20qM+THbxpoulZbnV7iOi5WLf5fuVChkCmQTefJjuRJD2YYHcgw0pvCsZ2JYximwZLzFnHRtatZtnYJK9Yv5Zx1nWddt+54PPnD1/j2V3/K+mtW8if/87MzFtSJUKI6CXyGj+UXLjlqGR4pJdnRHL17BujbO8Bg9whD3SOkBjKkBjLs395NPl2gXJi6q73h9xGpCxNLRki2Jlh92QqaOhpoXtJAy9Im2le00thRPz9Xlj8NOI7L//rmP/PYd37FxuvX8JX/8TunXFCgRDVrCCGIN8SIN8RYc/nkLuC2ZXvPtgoVqmUL13FxHRehCTRdw/D7CIRNzJCJP2As6Ievp5JCrsx//fwjbHphB7d/5ioe+o934zNOPrLvdFCiOs34DB+RhI9I4tixJRQzp2tnH3/6+9/nUNcIv/ef7+X2z1x9Wo+vRKVYMLiuyz9//1W+96f/TCQW4k8f/RxrL19x2uuhRKVYEIwMZPjLL/6Et1/excbrVvOF/+8BEvVn5pmiEpViXuM4Lk/+8DV+8N+ewrVdfv/rv8X/9qnJo/aeDpSoFPOW3e928+3/55/Ys72H9des5Pf/y320dR47uOjpRIlKMe8Y7s/wyJ8/zfM/3UyiIcqX/ubTfOz2dXNmpFSJSjFvyKYL/OPfPs8T338VKSX3PHQt//vnb5pVX6jZQIlKMefJZYo88b9e4WcPv0S5UOG6ezbwqS/cTPMcnVmvRKWYswz3pfn5917mmUffoFSocMXNa/n0v7uFJStPXzSqk0GJSjHn2Lu9h8cffpmX/3kLUsI1t6/j/s9dz9Lz2s501aaEEpViTlAuVXntqa0886M3eP/tLgIhP7d/5mru+uzHaG5PnunqTQslKsWc4I/v+xZ7tvWwaGkjv/snd3Lj/ZfOzrI2ZwAlKsWc4MF/ezPBiMkFly6fM0PjJ4sSlWJOcOkNU1+jea6jHHEUM0ZKSS5TYLBnlErZ84h+66WdfO/rT/Depv1nuHanH2WpFJNiWw6poSxCE9Q1RPEZOt17Bnj313sYHcxywWXLufiaVfz6X7az5ZVdSFdy7Z3rSTbH6d4zwNorzmHPtm6sisW6q1ee6dM5bcx7Uf38ey+zY/N+LrxiBRdcupyOFXMnEMt856VfvM1bL+2krbORC69YwYVXrGDoUJrfPL8Dq2qz8qLFAIyN5Lj+nksIhk269wxwYPcAftPgko+vppAt0b1ngHVXr0RKOe/vlwBOFNdl3ouqWrHYvfUgrz39LgDRRIjVG5ayan0nKy9czIq1HfN2FOlMkh8rUi5V+eJffop3f713ouFavqadz37lDoq5Mt17Bnnj2e0kGqNUyhZN7XXYlkMwbDJUC0JT1xjjUNfwGT6b2WP3+308/LcvHLfMvBfV/b93A/d97noGukd5b9N+3tu0jx2b9/Ob53dMlGld0sCKC9pZvqadZWsWsXRVG8nm2IJoNU8VQtOolCykhHA8iFX1FmWoa4xS1+gtWJAZzZNNF1h8TjPvv32AYNjPSH+Gmz55Gb/6+ds8+lf/gnQlV992kbfPefx7H9g/zA8efpnXXtpFPHH8RnrBhijLZYp8sK2bvdt62LO9h73v9TLYk5r4PJoIsWRlK4tXNLN4RQvty5toX9pIQ1udCqSCdz/1wmObaWhLYJoGrz39LlffdhGr1i3hmUffoP/gCNWKze/+yV2UCmUe/58voft0VlzQwWU3nk96OMfOLV20Lm6YNzMhjkVv9yiP/N0r/Oq5HQSDfn7rgcu497cvJRwJqLh/4HVpunb107WzjwO7+ji4e4DuPQPks4fX4fUZOs3tSZo7kjS3J2lcVEdTWx31LXEaWhMkm2KzsoTlqcaq2qSHc15Ys4ExRvozDPamGDqUZrA3xW3/x1Xc8sDxl7BJD+f4wX97irbOBlZvWEbP3kFueeBydr1zADPoJ14XJrlAA3Pu2zPITx55nVde3Ilh6Nx130buf/AyYrVbCRVM8zhIKUkP5+jdN8ihrhH6Dgwz2JNioGeUoUNpxkbzH/lOIOSnrjFGoiFCPBkhlgwTS4SJxIOE40EisSDBcIBQNEAg6McMGphBP4bfV0s6mq6j6wKhCYQQtQXDQLoS23ZwLAeramNVbSpli0qpSrlYpVSoUMpXKORK5LMlCtkS2XSBbKpANl0gM5InM5Ijmy4cs95Ni5K0dCT5xP2XctWtF57S33a+IaXk3S0H+ccfvcHmN/cRCvm5/Z4N3PvJjdR9KNy3EtUMKJeqjPRnGK219qmhLKmhLJmRnHcBj+bIpYtkMwWsin3a66dpgkgiRKwuTDwZ8YReHyHZFCPZFKe+JU5ja4L6ljjRRGhe39ecKqpVm1de3Mnj/7iJD3b1k6gLc/f9l3DHPRuITOKrpSLUzoBA0E/7sibalzWdsGy1bJEfK5LPligVq5TyZcrFKuVSlUqp6lmeio1juzi2g+O4noVy5YTFEprA59PRfdqEZfNWrvcTCPkJhkyCEZNwNEgkHiQYNpVQTpKhwTGe+vkWnn5iK5l0gY7F9Xz+i7dw461rMc2TD7qpRDWL+AMGyUB8wd5nLAQcx2XL5i6e+vkW3njtA6SUXHrFCu78rQ2sv2QZmjbzBmpGohJCJIF/ADqBA8D9Usr0McodAHKAA9iTmU2F4lTR25Piuaff5blfbmd4MEsiEeK+By7ntrvX09J64oX4psNMLdWXgReklN8UQny59vpLk5T9uJRyZIbHUyimTDZb4uXn3+f5X27n/fd60TTBxZcu41//wQ1ccc1KjFMUBnqmoroTuLa2/QPgJSYXlUJxyikUKrz52ge89ML7vPXmPmzbpXNZI//q967j+psuoKH24PpUMlNRNUsp+wGklP1CiMnu5iXwrBBCAt+RUn53sh0KIR4CHgJYvHjxDKunOBsYyxR547UPeO2lXWzZ3IVlOTQ2Rbnrvo1cf9P5LF9xcmsjnywnFJUQ4nngWKsrf2Uax7lSStlXE91zQohdUspXjlWwJrjvgjekPo1jKM4i+g+leeO1Pbzx6m62vduN60iammPcce8Grv74Ks5b0z4rgw4nwwlFJaW8YbLPhBCDQojWmpVqBYYm2UdfLR8SQjwObASOKSqF4lhUKhbb3unmrd/sY/Mb++jpHgVgydIGfvvBK7jyYys5d1XrnHi8MNPu3xPAZ4Bv1vJffLiAECIMaFLKXG37RuBrMzyuYoHjupL9ewd5560u3t7Uxfat3VSrNoZf58J1S7jt7ou59MpzWDQHg8LMVFTfBP5RCPFZoBu4D0AI0QY8LKW8FWgGHq+1ID7gUSnlL2d4XMUCw3FcuvYOsf3dbrZv7Wbb1m7GMkUAFnc2cNvd67l44zLWrltC4DSshjgTZiQqKeUocP0x3u8Dbq1t7wfUJDPFURQLFXbt7GPHth7e397L+9t7KRY9V/yW1jgbL1/Oug1LWbehk4bG2Bmu7fRQMyoUp5xq1aZr3xB7dveze2c/u3Yc4mDXMFKCELBkaSPX33QBa9a2c/7aDppn+WHs6UaJSjGrZNIFuvYNsX/vEPv2DrJvzyAH9w/jOC4A0ViQVWvauObj57FqzSJWn7+I8DxwpZkO815UTz/xDju29dC5rJHFSxpY3NlAU0tcORqeQqSUZNJFeg6O0H1whINdIxzsGubA/mHSqcMuJ8n6CMtXNLPx8uWcc24L565spaUtMSdG6E4l815UoyM53vrNfp59etvEe4Zfp7WtjkXtSdra62hdVEdrW4KW1gTNrfEZzUA+W3Acl9HhHAP9Gfr7MvQfStPfl+ZQT5pDvSnyufJE2UDQYElnI5dctpyly5tYuryJZec0U5c8OxcLXzD+VNlsiZ6DI/QcHKXn4CiHelIc6knR35em8iE/p0RdmOaWOI3NMRqbYjQ2RalviFLfGKW+PkJdfYRQyL9gW9Rq1SaTKjA6mmd0JMfIcI7R4RzDg1mGhrIMD44xPJSb6LKB57fV1ByjrT3JovYk7YuTdCxpYPGSehqb42fsQeuZ4qx2UpRSkhrN09+XYbA/w0BfhqHBLEODYwwNZhkeylKqjTodiWn6SNSFSdSFiSdCxBNBYvEQ0WiASCxIJGISjgQIh02CIT/hsEkgaBAI+DEDxim9yKSUWFWHcrlKuWRRLFYpFisU8hWKhQqFfJlcrkw+VyY7VmJsrMhYpkgmXSCTLh5lZcbx+TQaGqM0NsVoaonT1BynpTVOc2uClrYEzS1xfL5TMwF1PnJWOykKITwr1BDl/LUdxyxTyJcZGcmTGskxOpInncozOpJnLFMknSqQTuU5sH+I7FiJctma0nH9fh+m6cMwffgNHZ+h49M950Nd19B0DU0IEN4I2HjbJl2J60ocx8VxXGzbwbYcrFqqVCwqZYuptIW6rhFPhIjFg8TiQZavaCGeCJFMhkk2REgmIzULHSGeCJ911uZUseBFNRXCkQDhSIAlU1iEuVq1KeTL5HMVCgXPGpRKFqVihVLJolyqUi5bVCu2l6o2lmVjVR3smkhcR+K6Lq7rKcN1JUJ4DYAQAk0X6JonPt2nYfh0DNOHYeiYpoFp+jADBqZpEAgahGoeweGISThsEokGiEQDBALGgu3CzmWUqKaJ3+/Dn4x8JBCIQjGOGndWKGYZJSqFYpZRolIoZhklKoVillGiUihmGSUqhWKWUaJSKGYZJSqFYpZRD38VimmQyhZ5fUfXccsoUSkUU+SxV7fx9UePvzQpqO6fQjFl1p2ziN+74wp+9B8eOG45ZakUZw2241KqVAn4DQyfzu6eIbbu6+OCpa2sXtJ8wu8va61nWWv9CcspUSnmNVXLJpUroeuCxvjhSc6/fv8AL76zl8tXL+H6dSvYtKubZ9/+AInkE+vPZWV7I2/sPEjA8PHO3kOUqhYXr2hHSjnjmf1KVIp5S65U4bFXt/FBzzAtySjXXngOa5e1srtniP19o9x5xRr2HBrh2bd3E/AbXLN2GW3JGLt6hxh6L49P0/jkx9fxq6172d7Vz8Ur2melXuqeSjFviQZNfufGS/jGZ29lZXsT+we8UNAD6Rz5cpULlrayqCHOjgOD+H06uqYRjwSQrkQTgmyxAkBdNEiutj0bKFEp5j3b9vczmMlx1xXnA1AXCZEv1QQTCSIExMMBDgykKFVsBjN5NpzbQcDv48k33+e9rgGuXNMJMCtOnUpUinlNz3CGn722nbXLWukeSvP2nl5WdTTS2VzHXzz2Cs9s3sU9V62lrT5OfyrLz17bRksySksyys2XrCJXrLC0Jcn6Wer6wVkQ+EUxfyiWqxwYTLG/P8W+/lHCAT//6pZLJy0vpeThZ37D1n19XLyindZkjLFimU9eexH5UoUPeodpiIdZ3FQ363U9qwO/KOYWtuPSn8rSM5yhezDNgcE0BwfTHBhMMZjOT5QzfDqXnXf8Rf+EEPzurZcd87NI0JxV6zMdlKgUs4qUkkyhTP/oGIdGshwaHaNvJEvvyBiHRsboH81iu4fjCYYDfpY017Hh3A46m5N0ttSxvLWe9sYEvnkaZXjei+pnr23n7Q96aa6L0FQXpSkRmUjJaGje/jFzESklY4Uyw2MFhjJ5htI5hjJ5BtN5BtI5L6WylKtHBy+NhwO01cdYtbiJG9avoKMpQUdjgsVNCRpi4QUX8WneiyqVLbK9q5/n38lj2c5RnwnhjQQ1xMMkoyGS0SD1sTB1kSCJaNDLw0Hi4QDxSJBo0DyrRCilpFCuMlYoM1YokSmUyeRLpHMlUrniRJ7KFRnJFhjNFo/5G9fHwjQnIixvTXLVmk5aklHa6uO0JqO0NcSJBs0zdIZnhgUzUOG6kky+xGDGaz1Haq3pSLbA6FiR0WyBVK5EKlegYjmT7icSNIkGTaIhL48E/USCJiHTTzhgEAr4CZt+ggGDoGEQMH0EDB+m34dpeMnv0/EbPgxdw6dr+HQdn66ha9q0AlZKKbFdF8eR2I4XN9ByHCzboWo5VG2HctWmYnmpVLEoVy1KVZtiuUqxYlEoVyiUvTxfqpIrVcgVK+RKFfLFylFdsSPRNUFdJEgyFp5ojBriYRrjYRrjERoTYZoSURrjYYyzMHLtWTFQoWmCZCxEMhbivMXHn8dVqlik80Uy+cOtc7ZQZqxQJlssky1WyBbL5EtV+kazFMpViuUq+VJ10otwOuiamAicKfhQhFq8KLWOdKcUhfZ4CAFh00846Ccc8BqHRDhIR2OCWMj0XkeCxEIBEpHAhNWui4aIBk0VsfYkWTCimg5B0yBoxmmrj0/7u5btUChXKVWtCctQrtqULbtmPbzcsj1LYjnuhJVxXYlTi0zrSomU0hNRbb7Z+CWsaV5IaF0bj1QrMGrWzvDpGD59whr6fTqBmpUM+A2Cfh9B07OoAcO34O5X5gNnpahmguHTSUSCJAie6aoo5ihnz125QnGaUKJSKGYZJSqFYpZRolIoZhklKoVilpmRqIQQ9wkhdgghXCHEMR+E1crdLITYLYTYK4T48kyOqVCcCaSU9IyN8YtdO/lPL7143LIzHVJ/D7gH+M5kBYQQOvBt4BNAL7BZCPGElPL9GR5boThljJXLbBsc4N3BAbYODPDuQD+jpRIAQd/xZTMjUUkpd8IJvSU3AnullPtrZX8C3AkoUSnmBGPlMjuGh9gxNMT2oUG2Dw5wcGxs4vPldUmu7VzKhS2trG9t5dz6Bow/+KNJ93c6Hv4uAnqOeN0LTOp5JoR4CHgIYPHi4/vTKBTTQUpJbzbLzpFhdg4Ps3NkiB1DwxzKZSfKtEWjXNDUzH1rLuDC5hYuaG4mZk5vQvAJRSWEeB5oOcZHX5FS/mIKxziWGZt0VpuU8rvAd8GbUDuF/SsUHyFTLvHB6Ci7R0bYPToykeerVcC7KDsTdaxrbeXBtWtZ09jMmqYmksGZz5Q5oaiklDfM8Bi9QMcRr9uBvhnuU6FASslgIc++VJp96VH2plLsS6XYm0oxXCxMlIv6TVY2NHD3qvNY2dDI6sZGzq1vIGQYp6Rep6P7txlYIYRYChwCPgkcP26uQnEE6VKJg2MZDmTSdKUzdGXSdKXTdGXSFC1rolzE7+ecZJJrlnRybn09K+rrObe+gdZI5LROLJ6RqIQQdwPfAhqBp4QQW6WUNwkh2oCHpZS3SiltIcQfAP8C6MDfSSl3zLjmigVDxbbpy+XozWbpzY7Rkx2jN5vlQCZD91iGbOVwTD5NCBZFYyytS3DJokUsTdSxPJlkeV2SpvDc8CJeME6KirmJ7bqMFAsM5vP05XIM1PL+fI5D2Sx9udxRXTUAn6axKBplcTzB4niCJYk4nYk6OhMJOmJxzBMMaZ8OFrST4jv9ffRmszSGwzSEQtQHQ8QDAbQ50GItVKSUFCyLVKnISPFwGirkGS4UGC4WGcznGSzkGSkWcT/UcJu6Tls0Rms0yrWdnSyKxWiPxWmPxVgUjdESiaBr83eyz7wX1U/f38GP39t+1Hu6ECQCQepDQRKBAIlAkLpanggEiAdMYmaAuBkgZprETJOoaRL1+zH0s8c13HFdCpZFrlIhW6mQq3r5WLnMWKXCWLlEulwmUy6TLpXIlMukSkVSpRIV59ghCeqDQRrDYZrDEVY2ePczzZEozeEIrdEILZEodYHAnOimnSrmffcvWykzkM8zXCgyUiyQKpUYLRVJl7wLIFMuky6XSJfKZMolrBO4w5u6TsRvEvEbhP1+QoafsOHFowgbBgGfQdDwEfD5MHUfps+HqeuYPh9+XZ9IPk3Dp2kYmhebwlfz5tWEQBdeKywECMSH3OklUoIrx13qJU4tVsV4shwXy3WoOodTxbYp11LF8fKSZVGybYqWRdGqUqhaFC2LfLVCwbImhpcnQwDxQIBEIEBdrUFKBkPUh4LUBYLUh0ITIhrvJZwtjdKC7v7FzAAxM8C5J142CCklRcuqtcJlspUy2SNa6Xy1Sq5SIV+1KFhVCtUqRcsiXS7Rl8tRtCzKtlXL7ckftp1h/LpOyDAI+HwEfQahWqOQDAbpiMeJ+P2EDT8Rv3/CQkdNc8JyxwPedtQ0VTf6JJj3opoOQgjCfj9hv5+2aHRG+5JSehbCsanYhy3GuAWxXZeq4+C4LrYrsV0HV4IrXVxZi1FxxL6O7A7ptaAwes2yaULg03R8Wi1WhaYdZRFN3bOSAZ9nOZUQzixnlahmEyGE1/Xz+eDsCmunOAHzd4hFoZijKFEpFLOMEpVCMcuoeyqFYhqUnSr7coPHLaNEpVAcAyklg+Ux9uYG2JsbYE+unz25AboLI7gneJiiRKU4q5FSMlLJ0ZUfois/xP78IPtqqWAfnsjbGqxjRbSFG1ouYEWslev400n3qUSlOCuwXYdDpTTdhWEOFIY5kB+mKz/EgcIwebs8US5mBFkeaebm1otYHm3mnGgLyyPNRI2pOy8qUSkWDLbrMFgeo7c4Sk9xlN5iip7CCN3FEXqLKRx5eIpavRmlM9zAzW0X0hluYmmkiWWRJpL+mfteKVEp5g1SSnJ2mf5SmkPFFH2lNH2lFL3F1MTrI4Vjaj46Qg0sizRzbdMalkQaWRJuYEm4kdg0LM90UaJSzBks12a4nGOoMsZgaYzB8hgD5TT9pQwDpQwD5cxR9zngddfagknOjbVyXfP5LAolaQ8l6Qg30GhG0cTpf2qkRHWWUXEsDE2fuNgc6TJSySGApoC3XldfMU3JqRLxmTQHExTtClvTBwjoBuvqlk67e2S5NqlqgdFKjtFKjpHxVM4yXMkxXMkyXB4jVS185LtRX4DmYIJFoSQXJ5fRGqyjLVRHW7CORcEkESMw499ktpn3otqWPsihUoqEESbuDxE3QsT9IcK6uaB9dk6G3uIoX3rnUb64+nYuquvElS6bRvbyTN9WokaA2xddTHuonu/te5HWYIKiU+UPz72Zl4fepys/hKkZ5O0K1zSdd8Jj/fstj9BTGGG0midrlY5Zps4fptGM0WBGOS+2iMZAjEYzRnMgTnMwTnMgQdg3/yZWzntRPdX3Do/3bPrI+7rQiBlBor4gMSNIxAgQ9QWIGEEivgBhnzmRh30BQrqfkM8kqPsJ+fwEdT8B3Y+pLYzVCMuOxc97NnNX+wZs13MwLNpVnhvYxtcuvJ+8Xea/73ySTy+9ho5QPb+z/Fq+t+9F9uQGeHNkD/9p7f1UHItv7Hh8SqIK6SadkSbW+5eRNCMk/REazCj1ZpRGM0rSjGBo8/7yOybz/qz+cOXNPNB5FZlqgTGryFi1yJhVJGsVGbNK5K0SWatM1irRV0yTt0vk7QpV157S/jUEpm4Q0A1MzfAcEzUDv+bDr/kwNB9+TcfQfBiajk/oGJqOLjzHRF3onuuG0BB4DooTa/0iPhoVUYKLt3Spi6y5ibg4RyTbdbCliy1rriauzVfPv5eEPzTpebyT6uLcWCslx6LkeBGINCGoOt7vYAidqmtTdKoT1iGsm5QdC6fm2KkL7SOu8ZPxtQvvn1K5hci8F1XEFyDiC7Ak3DCt71Vdm4JdpmhXKdhlCnaFklOlYFcoOxZFx8vLTpWSY1FxLMqORdW1qLied23VtcjbJSzXwXJtbOl55FrSwald+OOCsGtevCd6Gn8kGp5flYbnT+WJc1ywOobQa97FPqwTNBJbUl1Y0mFPrp+EEWJj/XIMTachEONQMUXeLtMRqqclkOCpwhb25QY5VEpx26KLWR5t4dWhXVRci7UJFTX4RMx7d/r5yLi4Jvvtx63ZqeDZ/ndJ+MM827+Nr55/D4eKKX7Y9Qqm5uN3ll1L0ozw0+43KdgVGs0Yty5aR6Za4PGezfg1H3d3XEJoHt7nzDbHc6dXolIoToLjiUq5figUs4wSlUIxy8z7gQqF4nRRssdIVQ8yWjl43HJKVArFEbjSIWsNkK72kK72kq50k6p6qexkT7wDlKgUZyFSuuTsYcaqfWSqh8hYh8hUe0lXDzFW7cPl8OOJoJ6gzt/OOZGrqDMXU+9fQp25mH97zCXbPJSoFAuSilMgaw2QtQYYs/rJVvsZs7yUtQZw5OEleHRhkPAvIulfzLLI5dT5O7xkthPU49M+thLOfPeoAAAK90lEQVSVYt4hpaToZMhZg+TtYbLWIDlriJw1WNsepOzmjvqOXwsRN9pI+pewLHI5caONuL+NhH8RUV8jYhZnsytRKeYUtlulYI9SsFO1fJS8PULeHiZv1XJ75ChLA2CIAFGjmajRTEtwFTGjlZjRTNxoJe5vxdSip20OpxKV4pRjuWVKzhhFO03JyVC0MxSdNCU7Q8FJUbTTFO0UBTtN5UMWBrzuWdhXT8TXQHNwFef4mogajUR9TUSMRmJG82kVzYmY96I6mN/MSKWLgB7F1KMEtAimHsXUI5haGL8WmpZpHyzt5vXhh4n721gR/RgdoXUIIchag2wa+XtsWWFj/adImovZMvpPFJwUphbhkvoHKDkZNo3+CNutsLH+QWL+yW9m5xtSSmxZpuIUqLgFKk6Ospv38omUPSqVnDFKThZblo+5T0MECPmShHx1JM0ltIfWEfYlCfvqa3kDEV89AT02ZwQzFea9qPbmX+e9zJPHKSHwa0H8WpigHuOBpd857v4kEl34qbpFokbTxJ+5JfVPbKx/EJ9msnn0x2yo/21y9jAbGx5k88ijFJ0M76R+ypr4zejCYHvmSS5v/D/RxOlbWkZKF0daONLCllUvdys4sootq1huGdutYMsy1kQ+nkpYbomqW6LqFmp5sbZdpOoUcDn2mlTjmFqUgB4jqEcJ+ZLUm50EfQmCepyAHiekJwj64oT0OkK+BIZ26lzazyTzXlTXNf8RVzc+RNnN1VrNPGUnS9Udb1ELE9tSHv+iAGgOrOTOjq9Tssd4deg7XN/6f6MLHyU7Q8RoRBM6JWeMrDVIzGgmqMeJ+9tqN8n9NJjLEUKQs4dOeCxHWvz04BeOek8CEs/VQkrXW68KB1e6SOng4uBKL0kcHGnjShtHWhPfmz5ew2NoQQwRwK+FMLQgMaMJf83a+/UwphbG1CL49fBRPYKgHsOvhU9rAzKXmfeiEkLg10P49RAYzbOyP4CgL07VLaIL7yfyaSautNGEji4MQnqCopMBoGhnCOoxdOE/vB/PceOExzP1CBL5obKa528ldG9RODQ0oSHQ0YSOEDo6tVz40IWBVsvHt33Cjy4MfJqJT5j4hB+fZqILvyceLYBPmPi1ILrwz6vu1Vxn3otqttmf+zUHCpuoOHkurLuTZ/v+jBvbvsRFdXfzq8G/RkrJ2ro7iPvbcNwqrw89jC0rxIwWLkjcxq8G/woJrI7ffMJ7OV0Y3NXxzdNzYorThnL9mAQpXYTQcKQ9Ya0st4xE4q/dC1huCUfaCDRMPewtMG2P4uIQ9TWp1n8Bs6CXJz1VjFuZcUEBGNrRkXsMLYhx1HcEEWN6HsiKhYcSlUIxRaSsgH0QnK7jlpuRqIQQ9wH/L3AesFFKecy+mhDiAJADHMCezGwqFLPBh9dQntZ33SI4PeB0g9ONtLvBOeiJye2DKcQYmamleg+4Bzj+wx+Pj0spR2Z4PMVZhpRVkDYIHSG82BjSzYO1HbQIwrgAKUtQeRPkGOidCP9FSGs3svgowtcJoQcRR4zMHgs399dQ+gm4H7pERQJ8HeBfj/DdA/pS8HUCF0y6rxmJSkq5E1A35IpTgnQGkPm/BmEizBvAvLImoOeR1g6EFkfKMmgtyMqvEP4NyMrL4FsMlRcQwbvBHYXiIxD+7HEtmNAXIc1rEXoH6B3ePvQlCG3uzlKXwLNCCAl8R0r53ckKCiEeAh4CWLxYhcM6W5HShcrLgIvQ2mDc0jijyOomtPg3kM4QMv8XiNCnEMZqRPAOKHwfrF1IpxfNf5EnzMqLJ3xiKEL3Irh3Vup+QlEJIZ6HY3pkfUVK+YspHudKKWWfEKIJeE4IsUtK+cqxCtYE913whtSnuH/FAkQ6AwjzJs9CZb6A8F8CwgBZ9QoIE8Znq8uaY6G0QIRhfPaMCDKV+6DZ5ISiklLeMNODSCn7avmQEOJxYCNwTFFNf98lwIcQxgnLKk4NUrog8+COgczW8jEvd9NIdwxkBtw0uF4uwv8aETqeZRBeVwzH+56IePvRYqB3IKubvP34N4DehrR/DKVfIN0hhLEGYV6Fm/2mt5/gfd4eF4rrhxAiDGhSylxt+0bga7O1f5n7cyg+ghRBEFEvaTEQEdAiXi4iCC3itWATKeS1YiJ0xPZ4Csyq09pcw3vgXwFZBlkCWazl49tFcIsgCyALSJkHt+AJR+bAzdXyvCcimee41kAEQcRBqwMtAcZq0I//PE8IgQzciMx9A6x3EOaVyPy30GJfhdBvI4s/Rmix2iBEAAI3g6wggncihA8ZuAmhLwYtDPryWf39TsSMZlQIIe4GvgU0Ahlgq5TyJiFEG/CwlPJWIcQy4PHaV3zAo1LKr09l/1OZUSErr4O1tdYa5mt/eO2PdvO1C6HgXSjTwgARqCUT8Hu58Ne2/V5XBKOW+2q5DsJXO1UdhI4XCW48F7UW88h01BkBbu3CH08O4Na6NA5g17btWrfHOiK3gKrXRZLV2nbliFQGKkyvS2TUGqnwEQ1XpJZHQcRrjVbCa9C0eE1EnpDGR+0WEipCLXgz1GWpJrJaK+wWD7fMslITXhlk2etWHnUhjl+c4xerdcRFe+SF7dQubJfDF7/rvT8hkumgHU5CxxOnrybc8W2j9tqoib6WCz9gHm4MhAkEapZ4vME40kKPW+2w91rzrPqJhqPPRtQ0JbwZ34gIEJla+VNUj6Mt0LjA5IeOeKRFU8w3zhpRzRUOd/0UC5WFezeuUJwhlKgUillGiUqhmGWUqBSKWUaJSqGYZZSoFIpZRolKoZhllKgUillmTk9TEkIMA8dftg4agIXgUbwQzuNsOoclUsrGY30wp0U1FYQQby2EmBcL4TzUOXio7p9CMcsoUSkUs8xCENWk8S7mGQvhPNQ5sADuqRSKucZCsFQKxZxi3olKCJEUQjwnhNhTy+smKXdACLFdCLFVCHFmVjn4EEKIm4UQu4UQe4UQXz7G50II8de1z7cJIdafiXqeiCmcx7VCiLHab79VCPEfz0Q9J0MI8XdCiCEhxHuTfD6z/0FKOa8S8F+BL9e2vwz82STlDgANZ7q+R9RHB/YBywA/8C6w+kNlbgWewfNivAz4zZmu90mex7XAk2e6rsc5h2uA9cB7k3w+o/9h3lkq4E7gB7XtHwB3ncG6TIeNwF4p5X4pZRX4Cd65HMmdwA+lx5tAQgjReroregKmch5zGunFnEwdp8iM/of5KKpmKWU/QC1vmqTceFTct2tRb880i4CeI1731t6bbpkzzVTreLkQ4l0hxDNCiDWnp2qzxoz+hzkZo+J4UXGnsZspR8U9TRwrMMWHh16nUuZMM5U6bsGbxpMXQtwK/BxYccprNnvM6H+Yk6KSx4mKK4QYFEK0Sin7ayb5mCtWy1MYFfck6QU6jnjdDvSdRJkzzQnrKKXMHrH9tBDib4UQDXL+rPoyo/9hPnb/ngA+U9v+DPCReO5CiLAQIjq+jRcV95gjPaeRzcAKIcRS4QXS+yTeuRzJE8Cna6NPlwFj413dOcQJz0MI0SJq8dWEEBvxrrPR017Tk2dm/8OZHok5iZGbeuAFYE8tT9bebwOerm0vwxuVehfYgbeYwlyo+63AB3ijZ1+pvfdvgH9T2xbAt2ufbwc2nOk6n+R5/EHtd38XeBO44kzX+UP1/zHQD1h4Vumzs/k/qBkVCsUsMx+7fwrFnEaJSqGYZZSoFIpZRolKoZhllKgUillGiUqhmGWUqBSKWUaJSqGYZf5/IYCPY0Sb8EQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output(SGDMomentumOptimizer([w], lr=0.15*(1-0.5), momentum=0.5), nsteps=10, fname=\"sgd_50mom_example.pdf\")\n",
    "output(SGDMomentumOptimizer([w], lr=0.15*(1-0.25), momentum=0.25), nsteps=10, fname=\"sgd_25mom_example.pdf\")\n",
    "output(SGDMomentumOptimizer([w], lr=0.15*(1-0.75), momentum=0.75), nsteps=10, fname=\"sgd_75mom_example.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "71AW8tPCXaBN"
   },
   "source": [
    "In the below example, we can see a much obvious positive effect of using momentum if we inject noise (increase non convexity) in our loss landscape. Momentum is able to ignore this noise more effectively than vanilla SGD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 748
    },
    "colab_type": "code",
    "id": "c2ATfhURcufu",
    "outputId": "32fce40c-0c5e-4dc5-d426-84ef30cc2196"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output(SGDMomentumOptimizer([w], lr=0.1, momentum=0.0), nsteps=30, noise=1.0, fname=\"sgd_noise_example.pdf\")\n",
    "output(SGDMomentumOptimizer([w], lr=0.1*(1-0.8), momentum=0.8), nsteps=30, noise=1.0, fname=\"sgd_mom_noise_example.pdf\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1sE4L-OyY03A"
   },
   "source": [
    "# RMSProp\n",
    "\n",
    "Now, we shall move into the realm of adaptive optimizers that try to do something clever by taking into account the past movement of the gradient for each weight. \n",
    "\n",
    "The intuition is that different layers of a neural network learn at different rates. For example, for a big convolutional net, the output is less sensitive to the pertubations of the weights of the earlier layers and more sensitive to pertubations to the weights of the later layers.\n",
    "\n",
    "Therefore, in some networks using a larger learning rate for earlier layers and a smaller learning rate for later layers could aid in faster and better convergence. \n",
    "\n",
    "One such idea to vary the learning rate is introduced by RMSProp. The key ideas was to normalise the learning rate of each weight by the gradients **Root Mean Square**.\n",
    "\n",
    "$$\n",
    "v_{t+1, i} = \\alpha * v_{t,i} + (1 - \\alpha) * (\\frac{\\partial{C}}{\\partial{w_{t,i}}})^2\n",
    "$$\n",
    "Here, $v$ is simply the *moving average* of the root mean square of the gradient. We use $v$ in our gradient update rule as follows:\n",
    "$$\n",
    "w_{t+1,i} = w_{t, i} - \\frac{lr}{\\sqrt{v_{t+1,i}} + \\epsilon}\n",
    "$$\n",
    "\n",
    "\n",
    "**Hint:** Use the state dictionary to hold the buffers for $v$. Keep in mind that originally the value of v should be 0 and the tensor should be the same shape as that of ```p.grad```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "mm6HE3kNZtO-"
   },
   "outputs": [],
   "source": [
    "class RMSPropOptimizer(Optim):\n",
    "   \n",
    "    def __init__(self, params, lr, alpha):\n",
    "        self.eps = 1e-8\n",
    "        defaults = dict(lr=lr,alpha=alpha)\n",
    "        super(RMSPropOptimizer, self).__init__(params, defaults)\n",
    "\n",
    "    def my_step(self, p, state, group):\n",
    "        lr = group['lr']\n",
    "        alpha = group['alpha']\n",
    "        grad = p.grad.data\n",
    "        \n",
    "        if 'v' not in state:\n",
    "            state['v'] = torch.zeros_like(p.data)\n",
    "\n",
    "        state['v'] = (1-alpha)*torch.pow(grad,2) + alpha*state['v']\n",
    "        grad.div_(torch.sqrt(state['v']) + self.eps)\n",
    "        p.data.add_(-group['lr']*grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 374
    },
    "colab_type": "code",
    "id": "FGvndDJ-c2-g",
    "outputId": "0f12938a-2426-4a53-dd6e-49236047ca56"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output(RMSPropOptimizer([w], lr=0.1, alpha=0.8), nsteps=30, noise=1.0, fname=\"rmsprop_noise_example.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JOhxGoIXqpkW"
   },
   "source": [
    "# Adam Optimizer\n",
    "\n",
    "What is Adam ? It is simply RMSProp + Momentum.\n",
    "\n",
    "The root mean square term is calculated exactly like as before\n",
    "$$\n",
    "v_{t+1, i} = \\alpha * v_{t,i} + (1 - \\alpha) * (\\frac{\\partial{C}}{\\partial{w_{t,i}}})^2\n",
    "$$\n",
    "The momentum update is given as below, it is roughly equivalent to the momentum in SGD.\n",
    "$$\n",
    "m_{t+1, i} = \\beta * m_{t,i} + (1 - \\beta) * (\\frac{\\partial{C}}{\\partial{w_{t,i}}})\n",
    "$$\n",
    "Finally, the weight update is given as follows:\n",
    "$$\n",
    "w_{t+1,i} = w_{t, i} - \\frac{lr*m}{\\sqrt{v_{t+1,i}} + \\epsilon}\n",
    "$$\n",
    "\n",
    "Is that it ? Well, not quite. Just plugging this in will give us nan values, to correct for this we do something called bias scaling. The idea behind bias scaling is simple. which just keeps the\n",
    "moving averages **unbiased** during early iterations. The algorithm quickly approaches the above steady state form.\n",
    "\n",
    "The equation of Adam with bias scaling is given as follows:\n",
    "\n",
    "$$\n",
    "b_1 = (1 - \\beta)^t\n",
    "$$\n",
    "\n",
    "$$\n",
    "b_2 = (1 - \\alpha)^t\n",
    "$$\n",
    "\n",
    "where $t$ is the step number of the gradient update. We use these values to modify our final weight update as follows:\n",
    "\n",
    "$$\n",
    "w_{t+1,i} = w_{t, i} - lr*\\frac{\\frac{m}{ b_1}}{\\sqrt{\\frac{v_{t+1,i}}{b_2}} + \\epsilon}\n",
    "$$\n",
    "\n",
    "And that's Adam !\n",
    "\n",
    "**Hint:** The torch operator [addcdiv_](https://pytorch.org/docs/stable/tensors.html?highlight=addcdiv_#torch.Tensor.addcdiv_) might be of some interest. Inplace ops are an automatic perf win !\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "wBY8z5kVZ7f8"
   },
   "outputs": [],
   "source": [
    "import math \n",
    "\n",
    "class AdamOptimizer(Optim):\n",
    "   \n",
    "    def __init__(self, params, lr, alpha, momentum):\n",
    "        self.eps = 1e-8\n",
    "\n",
    "        defaults = dict(lr=lr, alpha=alpha, momentum=momentum)\n",
    "        super(AdamOptimizer, self).__init__(params, defaults)\n",
    "\n",
    "    def my_step(self, p, state, group):\n",
    "        lr = group['lr']\n",
    "        alpha = group['alpha']\n",
    "        momentum = group['momentum']\n",
    "        grad = p.grad.data\n",
    "\n",
    "        if len(state) == 0:\n",
    "          state['step'] = 0\n",
    "          state['m'] = torch.zeros_like(p.data)\n",
    "          state['v'] = torch.zeros_like(p.data)\n",
    "\n",
    "        state['step'] += 1\n",
    "        m, v = state['m'], state['v']\n",
    "\n",
    "        bias_correction1 = 1 - momentum ** state['step']\n",
    "        bias_correction2 = 1 - alpha ** state['step']\n",
    "\n",
    "        m.mul_(momentum).add_(1 - momentum, grad)\n",
    "\n",
    "        v.mul_(alpha).addcmul_(1 - alpha, grad, grad)\n",
    "\n",
    "        denom = (v.sqrt() / math.sqrt(bias_correction2)).add_(self.eps)\n",
    "        step_size = lr / bias_correction1\n",
    "        p.data.addcdiv_(-step_size, m, denom)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "spCr1Z3ytVrI"
   },
   "source": [
    "As we can see, the updates are much smoother than RMSProp and we get the same benefits of adaptive learning rates !\n",
    "\n",
    "The situation is not as clear when we train deep neural nets. Remember, for some problems a well tuned SGD + Momentum outperforms many of the state of the art optimization techniques :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 374
    },
    "colab_type": "code",
    "id": "5atLfzHMNLMG",
    "outputId": "30f6f9ea-94f9-47e2-c9f4-a8fd1cdd9361"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VXN5uHqOlMjA4CKbkDOe/B09vN4/RUhkYHARKfHJ0u3mOUF0MDI4bjJbqGKDK4+Ffy5ZS0drKKb0LuHL4CEyKQp3Px98Xf0NLKMSt4ybQPy2Nt1avpNLjIdlq46ejRhOKxXjhuyX4wmF+NvokclxJ3X06PR5DVHGklPgjEbzhcDyF8EUi+CMRfOEw/vh6MBolGI0SiOrroWiMUEx3VgxFY0Q0jXAsRlTb7ZqhEdMkUU1DkxoxKXUnxfjyhwihe1gpQqAqgsenns24vLx2656blMQDp09ECMF9X84mHIthUhSeX7qEy08cgcti4dWVy7lu9Bg2NjRw7cjRvLxiGU3BIO+sWc3I7BysJhP/t3YtN4wZi0Xt/gmrPZljTlSalDQHgzQG/DQGAjQFAjQFAzQFgrSEgjQH9dQaCtIaCrUlbzi834t8f6hCYDebsaqq7mFrUrGoqu5npaqYVQW7yYpJUTCruveuquhOiru9eBWxW0D71l/GlzFNw221dqpOC3eW89Q3i7h02IlY46Ko8Xnpm5qKRVWp9fkob2khL8lNYUoKfVNSqfS0sraulpvGjEVVFN5avYqOvBZ2tbaiKoI0u8MQ3wHo8aJ6feUKZm3eRL3fT73fT1MwcEBxWFSVFJuNFJsNt9VGriuJwekZJFmtuK1WkixWnBYLLosFp9mCy2LGYbbgtJixm8w4zGbsZjNmJbHOh4ngtIJCTiso5KaPP+SSocMAsKpqm0hUIUi122kJ6e4WLaEgLos13iJ+/2itdHBe98/5gvnlety7JIuVdIedTIeTDIeDTKeTTIeTLKeTbJdLXzpdpNhsR93v1ZX0eFG1hkL4IxEKkpMZnZtLhsNBmt1Omt1Bqs1OusNOis1Oqs2G3dwznRM7YknlLj7btIlwLMb4vHzunj2Lx6dO45qRo/nfuV+jScklQ4fRLzUVbzjMk4vKqPf76e12c+nQYfxhwTwApg8YiLmD1uemseM4q/8AGgMBGgJ+GuI3sw0N9SwoL8cT3tfr2qqqZLtc5LqSyHG5yE1KoleSm15JSfRKSiIvyU1SJ1vknoDhpHiMoLvaSxQhCEWjbTeQpkCAmJSk2+0IIWjw+wlEI5gV/UKPaRrr6uuIahrDMrM6FFVHBKMRan2+tlTt9VLj9VDl9VLt9VLl8VDj8xLV9o63kWy1ku9OJs/tprc7md7JbgqSUyhITiHf7T7qupqGk+JxgO5qr3ex9myRU+17v5Uw3eHY67OqKJyYlZ2wethM5jYxHIiYplHv91PpaWWXx8Ou1lZ2eVqpaG1la1Mjc7dvIxT7fiqQIgR5SW76pKTEUyp9U1Ppl5pKXpJ7r+7r0YAhKoMjjqooZLtcZLtcjM7dd7uUkjq/blgpb2lhR3MT25qb2d7czLL16/CGw215LapK35RU+qel0T81lQFp6QxIS6dfaipWU/dc3gkpVQjxInAeUCulPHE/2wXwJHAO4Ad+KqX87of5DAxAb3WznC6ynC7G9tp7OEFKSb3fz7bmJrY1NbGlqZGtTU2sqa1l1uZNbUYqRQgKk1MYlJ7O4IwMBqdncEJmJgXJKR0aYw6XREn5JeBp4JUDbJ8ODIynCcA/4ksDg4NCCKFbGZ1Oxuft/VqcUDTKtuYmNjU0sLmxgQ0NDWxoqGf2ls1tDvcOs5lB6emckJHJCZlZDMvMZHBGJg6zmbKyMkpKSiguLqaoqOiQ65gQUUkp5wkh+rSTZQbwitStIouEEClCiFwpZVUiyjcwALCaTAzJyGRIxt5ewIFIhI1xga2vr2N9fR2fbtrIm6tXAXqrllbfwPI//JFYNIrZauWz2bOZdPrph1SPI9XpzAN27vG5Iv7dPqISQtwI3AhQUFBwRCpncGxjN5sZmZPDyJyctu+klFR6PKytq2VNXS2f//Z/0SIRNCAUCnHJH//AuB1bGZmdw8icXEbn5DIwPR1TJ4wiR0pU++vE7teWL6V8HngedJN6V1bK4PhFCEGe202e283UqmomzJ3HXCEIKwoms5mfnD+DVlcSc7Zt5d21awCwm0yMyM5hVM5+rCt7cKREVQHs6becD1QeobINDA7MggVw9tkUFRYy5/HHKVm9eq9nKiklO1tbWFZVxfLqKpZXV/PisqXtHjJhg7/xZ6pPDmD9Oxe4Dd36NwH4m5RyfEfHNAZ/DbqUuKDIz4evv4bc9lug3YSiUWxmc9cO/goh3gSKgQwhRAXwG+LBvqWUzwIz0QW1Gd2k/rNElGtgcMgcoqCADse/EmX9u6KD7RK4NRFlGRgcNochqM5wdM3vMDDoarpYUGCIyuB44ggICgxRGRwHlJWV8ehNN1E2dWqXCwqMCbVdjpSSaCzuVh/TXes1TX/v737d6dHd6IUQqKruLayqCiZVOepmY/cEysrKmDxpEuFQCIsQzHn8cYq6UFBgiKoNTZP4QmFafUFa/UE8/hCeQAhvIIwvGMIfjOANhgiEIvjjKRCKEAxHCIajhCJ6CkeihCIxIrEYkWiMmJa48WshwGJSMasqFrMJi1nFajJhtZiwmk3YLCbsFjMOqxm7zYzDasFhNeOyW3HaLLjsFlx2K0l2K26HDbfDSpLDhkk9dsVa8tJLhEMhYkBYUShZvZqi88/v0jKPWVFJKfH4Q9S3+qhv8dHo8dPQ6qfR46fJE6DJ66fZG6DFF6TZG6DVH+owRoXVrLZdqHabBZvZhM1iJiPZii1+Ye++0M0mFbNJxRRvZUyKvlQUgaLsfqk2ulL2rLemt2Capjsd6q2bRjSmEYnqwWTCEV2woWiUUFzQwXCUYDhCqy+oCz4cwR8M4w+1/+5eAJfNQrLTRrLLTorTTmqSnVSXnbQkB2luB+lJDtKTnaS7HaS6HD1HhAsWUPzKK1jiMyUsFgvFxcVdXmyPF9XKrVWs2V5NdZOH2mYvNU0e6lt81LV4CUX2jXltUhRS4hdNisvOwPxMUpw2kp32tju326HfyXff2Z02C0675bC9YrsDTZMEwhG8gVA8hfEEQrT6g/FWOUSLb/fNJUizL8C26kaavH6C4eg+x1OEIM3tICvF1ZZyUpPITk0iJy2J3DQ3GcnO7hfewoUwffoBZ0p0JT1eVJ8tXs/bJcuxmFSyUl1kpyQxvG8uGclOMpOdZMRTWpKDdLcTt6Pnv6j5YFAUod8UbBayUw8upl8gFKGh1UejJ9DW4u++YdU2e6moa2bJxgq8gb3jUqiKICsliZd/dTkZyc5Enk7nWLhQt/L16gVff01Rbm6Xd/n2pMeL6obpE7jxnAmkuOzHlViOBHarmfzMFPIzD+waD+ALhqlp8lDd5KG60UNlQytVja0ku2zt7lfb7OWDhavZsLOWM0cP5Kyxg9p6A0s3VlDZ0MK4wQXkpCXhC4YJR6LYrGbslnYC+PxAUF1p5TsQRuAXg27FFwwjpeTFWd8ydcwgTijI5uvlm6lsaCUYjuK0W7j49OF8uHA1W6oaCYWjXDN1DL2zUnj1i6WsLa/hx8WjGDMwH0pLYdq07wXVq1eX1bu9wC895InT4FhESonTZuHLZZvIz0whO0Xvnpau3U7R0EKumz6eXfUtfLdpF95gmNtnnMrQwixCkSj/nrWYwb2z+OWlxXy3qYLK2V/rgsrN7XJBdYQhKoNuQwjBO3NXYDObmHHKMNLceqSncCSGy67HAQyFo8Q0DZvZhElVcNgsBCNRymub6J2ZTGaKi9oNW4j+7Ge6oEpKulVQcAw8Uxn0XL5YupH3FqxiSO8sBIJ1O2u49YJTmTiyPyUrtpDispGTlsQJBdl8s66cFl+QbVWNjOzXC7vVzOqVK3j1P29RucmDKyUZZs/sdkGBISqDbmTKSQMpGlpIKBJFk5JeGW5MqsLpw/sye8lGapt9XHjKiaS67PTOSuGtkuV6eLPUJIakCm55+B9oUhLYsYYr//p7Tu3gRQ6ffLOWgb0yGJCX0aWzUwxRGXQbQghcdmtbVy8z2QWAWVU5d8IJe+W95PQRe31ev+wbKss+RpotaEEv89au5dQZMw5YVqsvyK9f+hzQB7tH9OvF6AF5nDQwj2GF2VjMiZOCISqDHkmx3Y4a8hMOB7DYbB3OlEhyWPnk4etYvmUXyzdXsmzzLp75aCGgz5QZ3rcX4wbnM3ZQb07sm3NYA/2GSd2g5xGLwejRlDU0UHLzzRRPmXJIMyWavQGWbd7F0k0VLN1YwcZddUgJDquZkwbmc/IJBZx8QiF9c9L2GQM1YqkbHFv8+9+wahVF77xD0aWXHvJhUlx2Jo0awKRRAwBo8QVZsnEn364vZ9G6chas3gZAdqqLohP6cMqwQiYMKSDJ0f6gttFSGfQsvF4YOBD69dOdDrtwFk1lQwtla3ewaN0Ovlm/E28ghKoIRvbvxb/u+rHRUhkcI/zxj1BdDe+/36WCAuiVnszFp4/g4tNHEI1prN5excLV25kfb8EOhNFSGfQcKipg0CCYMQPefLNbq2JMUzI4NnjgAdA0ePTR7q5JuxiiMugRlP373zz6yiuUXXIJ9OnT3dVpF0NUBkc9ZfPnM/n663kQmPzee5SVlXV3ldrFEJXBUU/J/fcT1jQ9zkQ4TElJSXdXqV0M65/B0c3771O8YAEWk4mwlEcszsThYIjK4Ohlyxb46U8pGjdOjzNRWnrE4kwcDoaoDI5OgkG49FJQVXjnHYr69KFo4sTurlWnMER1EEgpjTgYR4o77oBly+Djj496a98POW5FFQ7p4bcs1u9/glAowvYtdVisJvr2zyIajbFu9S58vhAZGUkMGJxDdVUzX8xcSXpmEtPOGYlqat/W09Lsp7amhUgkRiyqEY3G9Jh+MQ2pyb1eJykAhEBVBYqq6JFpTQomk4rFYsJsVrFYTdhsZqw2MxaL6dgU+WuvwfPPwz33wHnndXdtDprjUlQb1lby5isLSUt38d+/nA5ANBpj0YJNLFuyDXeyA78/RHZOCrM/W8mgIbmsWbWTvII05n+9joK+GUTCMWZ+vIzzLxrTbllff7GGZ/7yeZechxBgs1uw2y3YHRacTitOlxWny4YryYbbbSfJbSc5xU5ysoOUVCcpqQ5S01zYHZYuqdNhs3Yt3HQTnHEGPPxwd9fmkDguRTV4aC9+fu+5PPfUF23ftTT7WbxoC3c/cD4tzX6ef/pLfvTjCfQfkM35F43h3TfK2LKxmm1b67j0yiJamv089/SXHYpqfFF/MrMuxWxRMZkUVJOK2hapViAQehMVb7L06LQasageez0ab90i4RjhcFRPoSjBYIRgMEzQHyEQCOP3hfD5Q/i8IRob6vF4gnhaA0TC+wYUBbDZzaSluUjPTCI9w0VmlpuMTDeZ2W6yst1kZSeTkuo4oi1h2Zw5lFxxBcVWK0VvvgkdvFztaKVn1joBCEWg7RHn3GRSiUT0LqHZrBKNxojFNITy/UWlmlS0mAbEu42dmDfZKz+NXvlpCa595wkGI7Q2+2lq8tHS7Kep0Udzk4+mBh8N9R4aGrxsXFdF6byNhH8QkdZqNZGdm0JurxRye6WSm5dKXn4qvfLTyM1LwWRKXMTestJSJk+bRjgWw2K1MmfHDoqOgngTh0KPF9XaVRWsXF5O+fY6yrc3ML6oP9dc37GVSItpBIMRotEYntYATpeNrJxkNqytpLU1wOATepGdk8zMj5axaOEmaqtb6X9xNiNGF/LmKwuJxTQmTh52BM7w8LDZzNhyksnKSW43n5SS1pYAdTWt1Na0UFPdQk1VC9VVzVRVNbNyeTkBf7gtv6oq9MpPpaAwg4I+GfTpl0lh30x6F6ZjsRz8ZVXy6KOEYzF9gDcapaSk5Kg3nR+IHi+qr75YzYf/WUJGZhIFfTJIz+g4tHFTo48Xn/2K2ppW3n9nMdVVzdx+19mcf9EY3n9nMQ6HhYsvn4DDaWXM+H54WgOcOnEwFquJSVOHsXzpdmw2MyNGFx6BMzwyCCFITnGQnOJgwOCcfbZLKWlu8lO5q5FdOxvZWd7Azh0NlG+vp2zhRrSY3morqqB3QTp9+2fRf0A2/QflMGBQNqlprgMXPncuxTNnYlEUwkL0iAHe9ujxrh9NjT4sFhVnByGGDbqOSCRGRXkD27fWsW1LLdu21rJ1Uw21Na1tedIyXAwanMugE3IZMjSPIZKI4zAAACAASURBVEN7keS2w86dMGYMpKVR9tRTlCxZ0iMGeNtz/ejxojI4evG0Bti6uYbNG2vYtKGKjeurqChvaHsU7Zvv5n9LnyazsZK6j78k58wJPWaIwBCVwVGDzxdiw7pK1q2qYMgTDzJmzVx+M/gKStOGkpzi4MSRvRkxqoARowrpNzAbRTk6RWYEfjE4anA6rZw0ti8nffsZrJmL/J//4brr7mDCyp2sXlHOqhU7WTh3AwDuZDujxvRhzLi+jBnfj+zc9t8+crRgtFQGR54FC2DSJDjrLH0a0g+ixdbWtLByWTnfLdnGssXbqK/zAJBfkMbYCf0Zd3J/Rp5UiNXazit1upgu7/4JIc4GngRU4AUp5R9+sL0Y+BDYHTHjPSnl7zo6riGqY5Bdu3TDRFISLF4MKe23PlJKync0sPSbrSz5dgsrlu4gHI5itZoYPbYvRacNpOj0Qe1bF7uALhWVEEIFNgJTgQpgMXCFlHLtHnmKgbullAc1kcsQ1bFF2dy5lPzkJxQ3NFC0eDEMO/hxvlAowspl5XxbuplFCzdSXdWCEDB0eD6nF5/A6cVDOhyTSwRdLaoi4LdSymnxz/cBSCkf3SNPMYaojmvKSkuZfMYZ+owJi4U5CRjclVKybUstC+duYMHc9WzdXAvAkKG9OOPMoUw884QuE1hXGyrygJ17fK4AJuwnX5EQYgVQiS6wNfs7mBDiRuBGgIKCggRUz+BooOSRR76fMRGLJWTGhBCCfgOy6Tcgm6uvO4NdFY3M/3o9875ex/NPf8nzT3/J8FEFTDl7OBPPPOGIjWUmoqW6FJgmpbw+/vlqYLyU8vY98rgBTUrpFUKcAzwppRzY0bGNluoYYeZMys47j8mKQhj0lmrOnC4d4K2saOTrL9bw5eerqChvxGIxcerEwZx1zghGj+2Lqh5eeJZu7/7tZ5/twFgpZX17xzZEdQywZg0UFUH//pQ98QQl33xzRGdMSCnZsK6S2TNXUvLFGjyeIJlZSUw/fzTTLxhFRqb7kI7b1aIyoRsqJgO70A0VV+7ZvRNC5AA1UkophBgP/AcolB0Uboiqh1NfD+PHg9+vW/p69+7W6oTDUcoWbGTWx8tZ+u1WhCI45fTBXPCjMYwa0+egZnN06TOVlDIqhLgN+BzdpP6ilHKNEOLm+PZngUuAW4QQUSAAXN6RoI5VpJTfewDHNH3Kzu6fos3rV8VkVlC68G1/XU44DBdfDJWVMHdutwsKwGIxMfHMoUw8cyhVu5r49MNlfPbxMhaUrKewbwYzLh7HlOnDsdsPz4HTGPw9SMKhKE11rTTXe2iu99LS6KW10Yen2Ye3JYC3xY/PE8TvDRLwhgj6w4SCYYKBMJFwlOgBnAb3h2pSMFtMWGxmbHYLVrsZu9OG3WnF6bbjSrbjcttxpThITnXiTnORku4iJcNFalYyDpe1e+bSSQnXXw8vvghvvAFXXHHk69BJwqEoc79ay/vvLmbT+iqS3HZmXDKWGRePJSXVecD9jLl/nURKSVOdh+ryBqp3NlC7q4naikbqqpqpr2qmoboFT7N/v/uazCpJKQ6cbjvOJJt+8bus2B1WrHYzFpsZi9WM2WLCZIl7/8Y9gIUQSCmRUvfzisU0YpEYkXCUSDhKKBghFAgT9IcJ+kP4PSH83iDe1gCeZj+hQHi/dbLaLWTkJJOek0xmbgqZealk5aWR0zuN7N7pZOWlYjInztGwjT//Ge66C/7nf+ChhxJ//C5ASsmaVRW8+3oZpfM3YrWaOPv8UVx6xcn7nR5liOoHxKIxKrbWUb6xmvLN1ZRvqqFiay2V2+oI+ve+QJPTXWTmppCRm0J6TjLp2cmkZblJyUgiJTOJlDQnSalO7M5uahWAcDCCp9lPa5OP5noPTXUeGutaaaptpb66hYbqFuoqm6ivbmnzXAZQVIWc3mnk9cuiYGA2vQdkUzgoh8JBudid1kOrzKefwgUXwEUXwTvv7DMFqSewY3s9775expezVgEw9ZwR/OSnp+0lruNaVAFfiC2rK9i8uoKta3exZe0uyjdVt3XDhBBk56eRPyCLvL6Z9OqTSU5BOjm908jKT8N2mP3ro4lYNEZ9dQs1FY1UlzdQtaOeXVvrqNhaS8XWWiKh793pc3qn029YHv2G9qL/sHwGDu9NegcDqWWvvUbJdddR3KcPRd99B84Dd596ArU1Lbz7+iI+/fA7pJRMv2A0V/30NNIzko4fUWmaxo4N1axZspUNy3awYXk5FVtq2X2OKRku+g3No98JeRQOzqHP4FzyB2QfU8I5VGIxjeryBnZsrGLHhmq2ratk67pdVG6rb/v9UjPdDB5VwKBRBQwd05fBowvbfruyd95h8uWX66GZbTbmfPXVUe9o2Flqa1p44+WFzPp4OSaTwoWXjueGWycfu64fOzZUsXTeelaWbWbN4m14W/RnnuR0F4NHFjDx/NEMGN6bgcPzScvu+jlhPRVVVcjrm0le30xOmTai7fuAL8SWNbvYvGonm1buZOPKchZ9sRrQnyMHjujNGX3NrH72V4Sl1GdMRCI9OsbED8nKTubOX53DZVeezCsvzOOd10vbzd/jRfXBv+Yy661F5PXN5LTpIxg2vh/DxvUjpyC9x3iRHs3YnVZOHN+PE8f3a/vO0+xn3dJtrP52K02zS5j05N+xSRBCRUiJqpjomzeEWEw77JkLRxO98tO497cXcskVJzNwyIMHzNfju381OxtQzSoZOT3Dge2YoqwMpk9Hc7tZ++jzvDF/JV9/XQItSaRYcnGnORk3aShFZ53ImIlDsDkO0fhxFHLcPFMZHEFKSvSQzLm5MGcO7DH5ubnBy7L5G1jy9Tq+/Wot3hY/FquZMcVDOG36SCZMGYbTbe++uicAQ1QGiWXWLN1k3q8ffPmlLqwDEI3EWLN4K6WzVrJw1koaqlswWVTGTjyBiTNO4pSzhmOxdZ8H76FiiMogcXzwAVx2me5gOHs2ZGZ2eldN09iwbAfzP13OvE+W01Ddgstt54wLRjPtxyczcETvHvMcbIjK4LApKyuj5MknKX73XYrGjYPPPoPU1EM+nqZprCjdzJfvfsvCz1YQCkboNyyP6VcUMemisTiTju44joaoDA6LsrIyJhcXEw6HsSgKcz7/nKIpUxJ2fF9rgK8/XMqsNxexZXUFNoeFsy6bwIXXTSS3MCNh5SSS9kR17Ng7DbqMkk8+IRwO62NQQlCyeHFCj+902znv6tN4eubd/PXjX3Dq9JHMfL2U6yf+nkdueYkNK8oTWl5X0+PHqQy6nuJFi7AAYVXt8jjng0cWMPgvV/Gze87jo5fm8elrC5n/6XJGnTqIK++cxvAJ/bus7ERhdP8M2uejj2DGDMpuuIGSvn2PeJxzvzfIzNdLee/5EprqWhkzcQg//dW5DBjevf5ZxjOVwaHR0gJDh0J6OixZApbumyMZCob5+OUFvPPMl3ia/Zxx/miu/eW59OrTPc9cxjOVwaFxzz1QXQ3/+le3CgrAarNwyU1n8u8FD3L57VP55ovV3DTlUV5+/FOCB/An6y4MURnsn7lz4bnn4M47Ydy47q5NG063nWt/eS4vzHuAM84dzVtPfcEtUx5jScm67q5aG0b3z2BfAgEYORKiUVi16qj2i1pZtomnH3iXnZtrOeP80dz68CW423GDTxRG98/goCi76SYe3bSJsjvvPKoFBTCiaCBPf/Yrrr5rOqWzVnLL1Mf4bt6Gbq2TISqDvSh7/nkmv/oqDwKT772XsrKy7q5Sh1isJq68Yxp//ejnON12HvjJP/jnwx8S+cGLwY8UhqgMvqeykpK77iIM+kBvOExJSUk3V6rz9B+Wz1Mz7+K8a07jvee/5t4fP0NjbWvHOyYYQ1QGOqEQXHwxxdEoFpsN9QgM9HYFVpuFWx++hPueuZYta3dx5wV/ZsuaiiNaB2NGRRfh9wSoLW+goaqJpupmmutb8TT68Db7CHiDhPwhwsEImqahxTSEoqCqCiaziZy+mdz0x590WMbaRRv5/OW5DD15ICefexLJGW6ikSgt9R5sTitOt6PzFb79dli0iKL//Ic5vXpRUlLSI15ofSDOOH80ef0y+e1/vcBdP/ob9//9WsZPPvhX9xwKhvXvMNA0jaqttWxfs5PtayrYuaGSXZuqqNxSg6fJt09+RRE4U5w4kmxY7VbMVhOqSUVRFaSmx/uLhmNk9k7j9x/d027ZTTUtLPxwMX1P7M2GJVvJLszg1BnjaG308uEzn7NjbQU//tUFDBzdl22rd7Lsq9W4UpyMKh5KVkEG3mYfsWiM5Ay3bjq/+Wa4/374/e+76ufqFhprWvjtf73A1nW7uOepazj93FEJOa7xzt8E0drgYdWC9awt28TGpVvZtGwb/tZA2/asggzyB+Uy8bIisgsyyCrIICMvjbTsZJIz3Tjc9oSFcq7b1YDNaWPYKYNZv3gLsagez8+d5mLGrdOY/943qKoeKHN5yRocbju1O+vZvrYCk8XEl6/NZ9WC9UwY7Gb6X25HnT4dftfhyy17HGnZyTz61q38+prn+MNtrxCNxJh04ZguLdMQVTtIKdm2aidlnyzl28+Wsf7bLUgpMVtM9BtZyOQrT2PA6D70G15AwQl52J1HzgdIarItqEpjVTPjpo1s2+Zr9hENR0lKc9JU20IsEuOUC8ayYfEWzFYT7z81i1GThnHZlWN4a+hFrMsayomvvw5qF0SrPQpwJtl4+LWb+fVPn+dPd76Gw2VjwpSu6woaovoBUkq2rtjB12+XseCDb6ncUgPA4LH9uOqBixgzZTgDx/TD0o0vcdbr05+v3ipl0/JtJKW6WPTpd+T0zUIIwa4tNQS8IWxOKxabBV+LH3eai9YGD736Z9Nc10paugMuvpimINhe+NNhORz2BOxOK7976Ubu+fHTPHrryzz+7u0MHNE1k3INUcUJ+IJ88co8Pn72C3as24VqUhk1aSiX3nUeReeNIe0ojNZ01X0X0lDVTHJGEt99uQohBLXl9ZR+uJjy9ZWk5SRz1jUTiYSivP/UZ2xfW8FJk4ejJGk8e9XPOGfdYrRz7yX11K7tDh0t2J1WfvviDfz8wr/wm5/9k6c+vavDqLuHwnFvqGht8PD+U7P46Nkv8DR6GTyuP9OuncgZF0/AnZ50yMeNRWNUba2hcksN1dtrqS1voKmmmebaVrwtPvytAYK+ELFIjFg0hlAEJrMJi92M0+3AkWQnOdNNanYyGXlpZBdmktsvi/zBvTrdzZRSIoSgflcjNeX1xKIxfKZmzpo4lbzYIKyKjV+/cA8XXzvjkM+zJ7JjQxV3XPAXhowu5Pev33JIsQkNQ8V+aG3w8M6fPuGjZ2cT9IUoOn8Ml911HkOLBh108BFN09j03TbWlG5g09KtbFmxg4oNlXuN6JvMKilZyaRmJ+NKdZKalYzNaaOiaQfbajbTL2cgvdMKCQXCBDxBvC0+qrfX0lTTQsAb3Ku87MJM+g4vYNCYvgweN4ARE4fuN6be7vPIyEsjIy8NgEcffJBAxMcGlqEKlY2Va4HjS1SFg3O55Xc/4q+/fIv/e/YrLrs1caEB4DgUlZSSue8u4pmfv0xrvYfiy4q44t4L6TMs/6COEw6GWfL5ChZ8sJjFs5bTXNsCQFpuKgNG9WHc2aMoGJJH3sAccvpmkZaTspflr6ysjFf+/nde/OxNYpqmxx8/wHtwvc0+qrfVUrmlhp0bdrF9TQVbV+7gm0/1wPlmq5mRE4dSdMEYTrtoQrtd1eIVK46YF+/RzFmXTWDJ1+t49c+fceo5I8nr2/moUB1xXHX/GqubefLWf1H28VIGjenHz5+9gf4jCzu9v6ZprJy7ls9fKqH0wyX4PQGSUp2MO3sU46ePZuSkYWT0SuvwOGXz5jH5zDMJxmLs/vVVVeWhhx7ivvvu63R9At4ga8s2snjWcr6Z+R0VG6sQQjBi4glMvXoiZ1xyMvY938g+fz6ccQZlV15JyYkn9ujB3UTQWNPC9ZMeYfiEAfzvv284qH3b6/7FXzZ2dKYxY8bIRLFi3lp5cc4N8tyka+S7f/5ERiPRTu8bjcbk7JdL5NUDbpdTlMvkjNSfyj9d/w+5+PPlMhKOHHRdHvnNb6QKkngSQki73S5LS0sP+li70TRNbl21Q770m7flNYP+W05RLpPnu6+Rz//qVdna6JEyGJRyyBAp+/SR0us95HKONd59do48u/cdcunc9Qe1H7BEHuC67XbhtJcSJap5//eNPMd5tfyvE++SO9ZWHNS+S2avkDeMvFtOUS6T/2/8vXLO6/Nl0B86rPqUlpZKu90uVZBWkDebTPK5G2+Uj/z+94clrN1omiZXzV8nH/3J3+RU9cfyovSfyVXTrtT/7s8+O+jjRcIRGY3GDrteRyPhUEReNe7X8t7Lnzmo/Y5rUX3+8lw5zXqlvOOM38iWBk+n96uvbJS/vfhPcopymbxm4O2y5O1SqWnaYddnN6Xz5slHnE5ZmpsrSwcNknaQagJarB+yZcV2efuoH8uHEPKfjt5yecmag9o/FovJh698Uv7+qr8dVOvek3j76S/k2b3vkFvX7ur0Pu2J6piepb564Xr+fNPzjJw0jEdn3os7zdWp/batKue2CfezeNZyfvbw5fxz1RNMvKwooSGJ5bJl4PPhu/Y6Pj7vR7q7hZSEQ6GEulvUtJTzwsp3+S2SWwKV3Dj5Dma+MKfT+yuKwsDRfSl5p4yXfvNuwup1NDH9qiLMVhOfv7UoIcc7Zq1/rQ0eHvnJ0+T0zeTXb9/Z6bGdNaUb+J/zH8PqsPDkwofoP7JPQuqyav46Ni7Zwubl21ixejlf7PgPMUD+4VEGMRKJgoqGWdOY9+Qi6mb9mr7DCxg4pj/DThlE/qBeBy9qKSn5xS8IaxoxQFXA3l/hLzc9T2uDhx//akanjnnZ3edTubWGtx//iBFnnLDXlKhjgaQUJyedPpiy2au46bcXHfbN85gV1bN3v0pzbQt/W/BQp10gtq7cwT1nPUxGfjp/mHU/OX2yDqsOa8s28Oaj77eZvhVVoXBoPsEkLzH0tw4qiuTki07iuv7XsGXOB1yztIRgnuBDTeOLV+by0d8/B6BwaD6X3HUBU68+A9XUyTl6jz1G8ZIlWEwm/bWhFgsPvfA/LHx+Of+6/01Us8qlvzi/U4e65YlrWFu2iT9d/ywvrf/LEZ3neCQ45ewRfPPlGrau3UX/gxxe2YcD9QuPhnSoz1S1O+vlNNtV8h93v9LpfWKxmLzt5PvlJTk3yMbqpkMqdzf1lY3y0Z88KaeIS+SPMn4m/3X/63LVgnUy6A9KKaUsffddaQepCCHNZrN87rnnvt95xgxZarHIR375Szl//ny5fe1O+eEzs+SNo+6SU8Ql8saRd8lV89d2XIm33tIfma+4QpYuXCgfeeSRtme1WCwmf/Ojx+V0+1Vy1+aqTp/Xyvnr5FTzFfKTf355UL9HT6BqR708u/cd8tPXFnYqP11tqADOBjYAm4F797NdAH+Lb18JnNSZ4x6qqF588G15luVKWbm1ptP7zHxhjpyiXCZnvzL3kMrczZw35ssL3FfL6dbL5YsPvCH93sA+eUrvuUdeCFIFqcBexonS99/XjRY/+F7TNDn33VJ5RcFNcoq4RP7lxmdlNHoAw8GCBVJarVKedppuSt8PdRUN8nz3NfKB8/7Q6XPTNE3eMu4+ef3IXybUaHM0oGmavHjYPfJv973dqfxdKipABbYA/QALsAIY+oM85wCfxcV1MvBNZ459qKK66aR75K+mPXxQ+9xWdL+8Zew9h3WxNNe1yHMdV8rbJtwrd26s3G+e0tJSaTeZpNhjnEoFefOPfiQfeeQRefPNN0tVCP17VZWPPPLIXvv7vQH59O3/klPEJXLOG/P3LWDTJinT06UcOFDK+vp26/vK/74jpyiXyYaqzrfMH/79cznVfMVB3bB6Cj+/8C+dNq23J6pEWP/GA5ullFullGHgLfadTDYD2N0XWwSkCCEO/Pq9w0BKya4tNfQ5saDjzHGikShblu9gZPGww3pI/ejvnxMKhLn7xf9H/sD9n15JSQlhKdtmUgghMAEvvvceDz7wAC+++CImi+WAMSLsThu3/PWn9B7ci/888dHumxZlZWU8+uCDlE2apGecOVMP19wOoyadCMCmpVs7fY59hunuErtdYo4lkpIdeFv8h32cRBgq8oCde3yuACZ0Ik8eUJWA8veiubaVkD9Ebt/OGxkUVeFvpQ/jOMwXjc1+uYRRk4ZROPTAfjrFxcVYLBZCoRBCCCbnDyJzRzlv4SMmJTIa48Ybb6CgoOCA04gUReH8W6bx9zv/zbZV5dT4Kpk8eTLhQAALMOfZZykaMKDD+vaLT9HaumoHE849qVPnmNNHnyNXta22U/l7Eo4kGzu3HP55JaKl2t+t/YcTCjuTR88oxI1CiCVCiCV1dXUHXRlnsh0hBJ5Gb6f3URSFAaP60Kt/zkGXtyd9hxewdWU5QX/ogHmKior461//iiIEMhZj/o51ZNEbveesoqoWrrnmGu6777525+Wt+2YjjiQ72YUZeusXDOphxRSFksbGTtW3saoZgNSszvuK7Y69cSSiwB5pIuEoFuvhtzOJEFUFsOetOR+oPIQ8AEgpn5dSjpVSjs08iPfJ7sZis5CRn8auzdUHve/hculdF9Da4OGDv81sN19DQwNS09CAsKLylOkapFKCyfQQTz+9/5nqe7Jt1Q7mvlPGOTdMwZnspDg5GYuUqEJgsVo7PfN8d7dv0Nh+ncoP33f7DvcGdDTibQngSj6ICFQHIBHdv8XAQCFEX2AXcDlw5Q/yfATcJoR4C71r2CKlTHjXbzcDR/dl2VerCYciR9Tt/cTThjDmrJH86/432LBkC7f8+VqyCva9MRQXF2MSAk1KTGYTf/tbMQ0NRRQXF9GensLBMO88/hFvPvoezmQHP7rzXPD5KHriCT2s2A03UDxtWqdmnmuaxvtPf0ZqdjIFJ+R1+hy//WwZVoeV/MFd8kjcrdRVNtFvaOd/iwNyIAvGwSR0695GdCvgA/HvbgZult+b1J+Jb18FjO3McQ/V+rd49go51XyF/OK1/VjHuphwKCzfeOQ9ea7jSnmu40r5wn2vy4aqxr3ylC5cKC0gBUiLxdLhXL9QMCxn/fsrec2AW+UUcYl86MdPyNqdccvebbfpRty5BzcU8Ok/v9SHEF4u6fQ+TbUt8hzXNfLJ2/51UGX1BHyegDy79x3yjSc/71R+2rH+JWRGhZRyJjDzB989u8e6BG5NRFmdYcyU4fQe3Iu3HvuQMy4ej8V25N6tZLaYueK+i5h81Wn8857XePuxD3jnjx/QZ3gBw04Zwoi+Lr5+6n59ihIQi8UoKSmhqKgITdPwNHqpLa+namsNm5dtY9N3W1mzcAMBb5B+Iwt5bPaDnDRlhF7YV1/B00/DHXfAGWd0uo4r5q7lubtfZfgZJzDl6s7v9/bjHxEJRZhxy1kH96P0ADav0u1o/Ycdfkt1zDopLv58BQ+c/xgX3DKV2578WYJr1nkqNlYy5/X5fDlzNp7ls/nvaBUKkrOQROIz/k51nYVbSyX0g5eXqSaVwmH5DD15EKdeNIExU0d8b/L3eGD4cDCbYcUKcHTuWaD0w8U8fMWT5PbL4g+zHiAzv32z+26WzF7B/ec9xnk3Tua/n77uoH6DnsDzv3ufT15dyFvLHsbh6tgKfFzGqBg3bSQX33kO//fXmQwZP5ApV53WLfXIH9SLQWcXcMsjrxCORpmtKDx7/2M8Ejbz7dJvGNBrEHmpBVisZqwOK64UJ1mFGeT0yaLghLz9trJlZWWU3HknxTt2ULRgQacEFY1EefeJj3npwbcZNLY/v//k3k4HtqnaWsNjP/07hUPzubET4ah7GlJKSj9fxehTB3VKUB1xzIoK4LrfX86m77bxp+v+QSwaZdq1xd1Sj5IvviAcjeombyHY5Yhw30N3H9KxysrKmFxcTDgcxmIyMUdRaM8sIaVkyewVPHf3q+xYW8HpF0/gly/+v73d7Nthx9oK7j3nUbSYxoNv3bHfADM9ne/mb6BmZyNX/2J6Qo53TPtTmcwmHvrwl4w680SeuOF53nzsQw61u7t6wXr+fONzzHrxa1obPG3f+1r8NNe1/7qWYlXVR6EU5bCDrZT84x+Ew2FdoFK263u1YckW7pn2MPef8yihQJjfffArfv3OLzotqDWlG/jFmb9Di2n86csHKRiSAMvYUcgHL5SQmpnE6eeNTsjxjumWCvRpPb97/26euP45/v3g22xYvIU7nrmO1OzOB1FsrG5m2+qdnP1fk1i3aBOr5q/n1AvHUbmlmkWfLGXZnNWMnDSMS35+HnPfLWP512uYcM5o+o0sJKt3BkNLl/JeSi7f/eL/MWnK5EMPtvLJJxS/8QYWIfj/7Z15nBzFefe/1T0997Wz9yWtJHQhJJCQBAKDxX2Em0AI2MYJCbGd+CB5fbyvnbxxYmMncWwnjvP6gMQ2Nr4gAsxhm/sUSCCEhJCEjpV2V3vvzuzcM33U+0fPriTQSrvakbS76u/nU5/qmamprp7pXz3V3fU8VRxFoIm+JM//ei2/+9Fz7HhjN+HKEB//1u1c9ReXjPnxgmmY/Pqbj/GTL/+a2pnV3P3o56mfXXt0bZ7kbH+rjdef28aH/+aKsjz4hZNAVABuj8bnf/wJ5i6bxX//7S/5s9M/y8f+5UNc/KHzxjTXr6+9H3/Iy6lnz2PLK9sxdDue37O/fIWZC5v4x0c+z6++8Qitm9to27aPp+57gVh9lIVnz+WxnzzIb367DXfDeVxStZIVy49yUerHH4cbb2TV0qU8/dWv8twbb4xMY+rZ28e6x9/kxTWv8dazW7AsyZwzWvj4t27nsttXExjHA81dG/fwzY/9kB0bWjnvhpV8+rt3TCio6GTGsiy+938fpKI6xLV/+sGyX1Ku3AAAIABJREFU1XtSiArsqUh/eNcfsPLyM/jmx37Iv9zxPZ66/yU++uWbWbjyyPPkRClmX7x7iJVX2MOERG+SM1bbFi85kCabynHDp67k3GtX8PJD63j9jTe4646/J24Nkul7mIZN59DyajOLz1s45navXbuW537wA1b/9KesWrKE7IMPU9GdZUmlwms/3sy9dz7A3nfsRc0a59Zzyxeu44M3rWL2krGHXgPbGv/qX3/DQ//xO8KVQb50/6c478azyhpCYLLx9IPr2bZhL3/9r7cSmOC8zwM5aUQ1zIyFjXzz2b/j0e8/xY+//ACf/sDfceYli7nlc9ey5PyFhzyJ5q84hWd+/jI7NuwmUhVi7W/eYObCJprn15PPFMhnCxhFg1hdlEDEz+wlM7n/7jXsGNqMMBXy5CkaBts3v8tN4SNHg93w9GZSA2nWP/8MX/re/8WwTDTgkrZ6crPuGikXjAaYv2IOl//pBay8YinN88fvct+zt48Hvv04T9z7DEbR4NLbP8iffe3WMcfzmKr0tA/wvb9fw6IVs7noxkOH7ztaTjpRgW21rvn4pVz8ofN49PtP8etvPcZnL/kK886czY2fvpJzr1v+vlvZt33xBuI9Q4Qrg7z5tD0F6tLbV/PTf3yQJ3/yPNd98gpUTeXeL/4cze0iGPWzNPUuP5UZvIoPoUFTY9Oo0WPXrl1rr164YAFb/+QbnD60iwI9GNjr71oIis0Kf/LXtzBzYROzFjdTP7v2qCyJlJJt63ay5ju/5YUHX0MIwcUfOo9bPncNjadMvzl978XQTf7pU/cB8Nlv31a2NcOGmbYPf8dDIVfkyZ++yIPfeox9O7vxh32cd/1KzrvxLJZeeBqae2x9j2ladLf2Eu9JEMoOMfPaC3j2jBX8Z74FM2/x4f99E9d/+Jr9Alq1ilWRCGvXrOGir32NomHYrhvA8llzeHnZmVz56MP2+273qGGhx4KUkt2b2nhpzTqe/eUrdO7qwR/yceWfX8h1f3k5Nc1jewg81ZFS8t0vPcBj973MF/7jI3zwmrG5vLwXJ0LtGDFNU77+5Cb5z3/6/+S1sT+Vl2h/LK+rukPe/eHvyKfvf2nMcQNfeflleff8+fIVRZGvfOUr0ud22zH9XC75/XPPlT5Fsd3lQb4C8u6S9y+l2H9333XX/rpeeeWg+BLjoVjQ5YZn3pbf++x98vaFn5GXaH8sL3XfKj932VfkE//9rEwPZcZd51RnOCLtvXc/MqF6OMzcP8dSjUIxX2TD02/z0pp1vPbERob6kiiKYM4ZLZx27nwWrDiFeWfOon5O7fsWHrjoggsoFgq4gduBH2IP4VTgIrebp0vPmVQh+MdbbmH11Vdz0R132A90J2CR4r1D7NjQyruv72bL2u1seeVd8pkCmtvF6atP5dzrVnDO1cvH9ThhOvH0g+v5xl0/4/yrzuDz//GRCQ37TsppShPF7XVz9h8s4+w/WIZlWWx/fTfrf7uRTS9s5fF7nmHNd34LgD/so2VRMy2LmpixoJGnNjxOUddHHAa57DLczzwzMoS78dvf5sXPfGZEQKs/+UlWrVrF0y0tY1oR3jQtBrvidO3uZd/Obtq3d7LnnQ72vN1O/z7bOVEIQcuiJi758Pksv2QJZ1y4aNqFFBsvv/vlq/zb537J6efM5W++Wf7rqANxLNVRYOgGe9/Zx7sbdrNr4x72bOmg9e12UoNpElY/b5jPYGGhCoVrFtxKuDJEb34fp81bwpJTz6C9fw/b9m5h2WlnctqCJaXV6SWWaaHrBoVskXymQCaRIRlPk+xPE+9JMNCdoL9jENMwR9qieTRmLmykZVETs5fMZO6yWZyytGXMsQ5PBh79yUt890sPsOz8+fztD+/A65u418LhLJUjqjIhpSQ5kKJjRzdPPfEUL7/6CnX+RsKyksHuBIm+JOl4hnxmdFf796K5XQQrAoRjQWL1UaI1EWqaq6idWUXdrBqa5tZT3Vx5VCsBngyYpsV/f/03PPj9Z1l50SK++P8+ittbHqdVR1STCEM37GdbmQLFvI5lWlimhVAEiqqguV14Ax48fg9urzatH74eSzKpPP/8qftY9/QWrr79A9z5d9fj0sYY2XcMONdUkwiX5iIYdRGMTr/AKZOF1q2dfO0vf8S+1n4+8Y83cvXt5x3X/Tuicpg2WJbFb370Ivd+7TcEw36+dv/HWbJq7nFvhyMqh2lBf3eCb3/2F7zx/DZWXngqd/3rrUQrT8xUK0dUDlMa07R49Ccv8eN/eQzLsPjLr/4hf/Chc0/otagjKocpy/a32vju//k1Oza3s+z8+fzlV26ioaXqRDfLEZXD1KOvK8F933icpx5YT7QqxOf/4yN88Oqlk+ZOqSMqhylDMp7hV//5FI/86EWklNxw52r++FOXldUXqhw4onKY9KQSWR757xf4n3ueI58pcOENy/nQXZdTO0ln1juicpi09HXGeeje53ni/rXkMgXOuXwJH/mbK5g5yUNOO6JymHTs3NzOmnue5/nfbEBKOP/qpdz88YuYtbDhRDdtTDiicpgU5HNFXnpsI0/8bC3vvNGK1+/m6tvP47o7PkhtU+xEN29cOKJymBR87qbvsGNTO42zqvnzv72WS28+qyzL2pwIHFE5TApu+8zl+IIeFp81Z9LcGj9aHFE5TArOunjRiW5C2XAccRwmjJSSVCJDT/sAhby9csnrz23l3q8+wtvrxr5I93TBsVQOo2LoJoO9SYQiqKgK4dJU2nZ089YrOxjoSbL47Dmcef4CXvndZja8sA1pSVZfu4xYbYS2Hd0sOecUdmxqQy/oLD1v/ok+nOPGlBfVQ/c+z5b1uzn9nLksPmsOzXNrj2n8gZOJ5x5+g9ef20pDSzWnnzOX08+ZS+++OK89tQW9aDD/jBkADPWnuOiGFfgCHtp2dLNnezduj8aKC04lk8zRtqObpefNtyMNTfHrJeCIi1xMeVEVCzrbN+7lpcffAiAU9XPq8lksWNbC/NNnMHdJ85S9i3QiSQ9lyeeKfPbbH+KtV3aOdFxzFjVxxxevIZvK07ajh7W/30y0OkQhr1PTVIGhm/gCHnpLQWgqqsPsa+07wUdTPra/08k9//n0YctMeVHd/ImLuenjF9HdNsDb63bz9rpdbFm/m9ee2jJSpn5mFXMXNzFnUROzFzUya0EDsdrwtOg1jxVCUSjkdKSEQMSHXrQXZaioDlFRbS9YkBhIk4xnmHFKLe+8sQdfwE1/V4LLbjmbZx96g/v/7XdIS3LeVWfYdU7h33vP7j5+fM/zvPTcNiLRw3fS0zZGRSqR5d1Nbezc1M6Oze3sfLuDnvbBkc9DUT8z59czY24tM+bW0TSnhqZZ1VQ1VDiBVLCvp55+cD1VDVE8Ho2XHn+L8646gwVLZ/LE/Wvp2ttPsWDw5397HblMnjU/fA7VpTJ3cTNnX3oa8b4UWze0Uj+jasrMhDgUHW0D3PdfL/Dsk1vw+dz84a1nc+MfnUUg6HUCv4A9pGnd1kXr1k72bOtk7/Zu2nZ0k07mRsq4NJXaphi1zTFqm2JUN1ZQ01BBZV2EqvoosZpwWZawPNboRYN4X8oOa9Y9RH9Xgp6OQXr3xenpGOSqD3+AK249fMDOeF+KH//LYzS0VHHq8tm07+zhiltXse3NPXh8biIVAWLTNDDnrh09/OK+l3nhma1omsp1N63k5tvOJly6lHCiKR0GKSXxvhQdu3rY19pP554+etoH6W4foHdfnKGB9Pu+4/W7qagOE60KEokFCccChKMBghEfgYiPYNiHL+DFH/Li9bnx+DQ8Pjea21VKKoqqoqoCoQiEEKWQwSAtiWGYmLqJXjTQiwaFvE4hVySfLZLLFMilC2RSOdLJHJlkjmQ8Q3IwQzKeIdGfJtGfIhnPHLLdNY0x6ppjXHLzWXzgytOP6W871ZBS8taGvfzqZ2tZ/+ou/H43V9+wnBtvWUnFe1ZBcUQ1AfK5Iv1dCQZKvf1gb5LB3iSJ/pR9Ag+kSMWzJBMZ9IJx3NunKIJg1E+4IkAkFrSFXhkkVhMmVhOhsi5CdX2UyroIoah/Sl/XHCuKRYMXntnKml+t491tXUQrAlx/8wquuWE5wVF8tZwQZRPA63PTNLuGptk1RyxbzOukh7Kkkzly2SK5dJ58tkg+V6SQK9qWp2BgGhamYWKalm2hLDlisYQicLlUVJcyYtnslevdeP1ufH4PvqCHQMhHMOLDF/A4QjlKenuGeOyhDTz+yEYS8QzNMyr51Gev4NIrl+AZ41Kuh8IRVRlxezVi3si0vc6YDpimxYb1rTz20AbWvvQuUkrOOmcu1/7hcpatmI2iTLyDmpCohBAx4JdAC7AHuFlKGT9EuT1ACnvxC2M0s+ngcKzoaB/kycff4snfbqavJ0k06uemW1dx1fXLqKs/9EJ8R8tELdUXgKellF8XQnyh9Przo5S9QErZP8H9OTiMmWQyx/NPvcNTv93MO293oCiCM8+azV/81cWcc/58tDKGgT6QiYrqWmB1afvHwHOMLioHh2NOJlPg1Zfe5bmn3+H1V3dhGBYts6v5s09cyEWXLaaq9OD6WDJRUdVKKbsApJRdQojRruYl8HshhAS+L6X8wWgVCiHuBO4EmDFjxgSb53AyMJTIsvald3npuW1sWN+KrptU14S47qaVXHTZacyZe3RrIx8tRxSVEOIp4FCrK39xHPs5V0rZWRLdk0KIbVLKFw5VsCS4H4B9S30c+3A4iejaF2ftSztY++J2Nr3VhmVKamrDXHPjcs67YAELFzWV5abD0XBEUUkpLx7tMyFEjxCivmSl6oHeUeroLOW9Qog1wErgkKJycDgUhYLOpjfbeP21Xaxfu4v2tgEAZs6q4o9uO4dzPzifeQvqJ8XjhYkO/x7BXtb266X84fcWEEIEAEVKmSptXwr8wwT36zDNsSzJ7p09vPl6K2+sa2XzxjaKRQPNrXL60plcdf2ZnHXuKTROwqAwExXV14FfCSHuANqAmwCEEA3APVLKK4FaYE2pB3EB90spfzvB/TpMM0zTonVnL5vfamPzxjY2bWxjKJEFYEZLFVddv4wzV85mydKZeMu0GuKxYkKiklIOABcd4v1O4MrS9m7AmWTmcBDZTIFtWzvZsqmddzZ38M7mDrJZ2xW/rj7CylVzWLp8FkuXt1BVHT7BrR0fzowKh2NOsWjQuquXHdu72L61i21b9rG3tQ8pQQiYOauaiy5bzKIlTZy2pJnaMj+MPd44onIoK4l4htZdveze2cuunT3s2tHD3t19mKYFQCjsY8GiBs6/YCELFjVy6mmNBKaAK814mPKievyRN9myqZ2W2dXMmFnFjJYqauoijqPhMURKSSKepX1vP217+9nb2s/e1j727O4jPrjf5SRWGWTO3FpWrprDKfPqmDe/nrqG6KS4Q3csmfKiGuhP8fpru/n945tG3tPcKvUNFTQ2xWhoqqC+sYL6hih19VFq6yMTmoF8smCaFgN9Kbq7EnR1JujaF6erM86+9jj7OgZJp/IjZb0+jZkt1aw4ew6z5tQwa04Ns0+ppSJ2ci4WPm38qZLJHO17+2nfO0D73gH2tQ+yr32Qrs44hff4OUUrAtTWRaiuDVNdE6a6JkRlVYjK6hCVlUEqKoP4/e5p26MWiwaJwQwDA2kG+lP096UY6EvR15OktzdJX88Qfb2pkSEb2H5bNbVhGppiNDbFaJoRo3lmFTNmVlJdGzlhD1pPFCe1k6KUksGBNF2dCXq6EnR3JujtSdLbM0RvT5K+3iS50l2nA/F4XEQrAkQrAkSifiJRH+GIn1DISzDsIxj0EAh6CQQ8+PxuAgEPXp+G1+vG49WO6UkmpUQvmuTzRfI5nWy2SDZbIJMukM0UyKTzpFJ50qk8yaEcQ0NZhhJZEvEMiXj2ICszjMulUFUdoromTE1dhJraCHX1EWrro9Q1RKmti+ByHZsJqFORk9pJUQhhW6GqEKctaT5kmUw6T39/msH+FAP9aeKDaQb60wwlssQHM8QH0+zZ3UtyKEc+r49pv263C4/HheZx4dZUXJqKS7WdD1VVQVEVFCFA2HfAhvs2aUksS2KaFqZpYRgmhm6il1KhoFPI64ylL1RVhUjUTzjiIxzxMWduHZGon1gsQKwqSCwWLFnoIJFo4KSzNseKaS+qsRAIegkEvcwcwyLMxaJBJp0nnSqQydjWIJfTyWUL5HI6+VyRfF6nWDDsVDTQdQO9aGKURGKZEsuysCxbGZYlEcLuAIQQKKpAVWzxqS4FzaWieVxomorHo+HxuPB4NTweDa9Pw1/yCA4EPQQCHoIhL8GQF69Xm7ZD2MmMI6px4na7cMeC7wsE4uAwjHPf2cGhzDiicnAoM46oHBzKjCMqB4cy44jKwaHMOKJycCgzjqgcHMqMIyoHhzLjPPx1cBgHg8ksL29pPWwZR1QODmPkwRc38dX7D780KTjDPweHMbP0lEY+cc05/Ox/33rYco6lcjhpMEyLXKGI162huVS2t/eycVcni2fVc+rM2iN+f3Z9JbPrK49YzhGVw5SmqBsMpnKoqqA6sn+S8yvv7OGZN3ey6tSZXLR0Luu2tfH7N95FIrlk2TzmN1WzdutevJqLN3fuI1fUOXNuE1LKCc/sd0TlMGVJ5Qo8+OIm3m3voy4WYvXpp7Bkdj3b23vZ3TnAtecsYse+fn7/xna8bo3zl8ymIRZmW0cvvW+ncSkKt1ywlGc37mRzaxdnzm0qS7ucayqHKUvI5+Gjl67g7juuZH5TDbu77VDQ3fEU6XyRxbPqaayKsGVPD26XiqooRIJepCVRhCCZLQBQEfKRKm2XA0dUDlOeTbu76EmkuO6c0wCoCPpJ50qCCfoQAiIBL3u6B8kVDHoSaZbPa8brdvHoq+/wdms35y5qASiLU6cjKocpTXtfgv95aTNLZtfT1hvnjR0dLGiupqW2gm89+AJPrN/GDR9YQkNlhK7BJP/z0ibqYiHqYiEuX7GAVLbArLoYy8o09IOTIPCLw9Qhmy+yp2eQ3V2D7OoaIOB182dXnDVqeSkl9zzxGht3dXLm3CbqY2GGsnluWX0G6VyBdzv6qIoEmFFTUfa2ntSBXxwmF4Zp0TWYpL0vQVtPnD09cfb2xNnTM0hPPD1STnOpnL3w8Iv+CSH48yvPPuRnQZ+nrNZnPDiicigrUkoSmTxdA0Ps60+yb2CIzv4kHf1D7OsfomsgiWHtjycY8LqZWVvB8nnNtNTGaKmrYE59JU3VUVxTNMrwlBfV/7y0mTfe7aC2IkhNRYiaaHAkxUL+KfvHTEaklAxl8vQNZehNpOmNp+hNpOmJp+mOp+w0mCRfPDh4aSTgpaEyzIIZNVy8bC7NNVGaq6PMqIlSFQ5Mu4hPU15Ug8ksm1u7eOrNNLphHvSZEPadoKpIgFjITyzkozIcoCLoIxry2XnARyTgJRL0EfJ5TioRSinJ5IsMZfIMZXIkMnkS6RzxVI7BVHYkH0xl6U9mGEhmD/kbV4YD1EaDzKmP8YFFLdTFQjRURqiPhWioihDyeU7QEZ4Yps2NCsuSJNI5ehJ279lf6k37kxkGhrIMJDMMpnIMpjIUdHPUeoI+DyGfh5DfzoM+N0GfB7/HTcCr4fe6CXjc+LwaPk3D63Hh1Vx43C48mp3cLhW35kJTFVyqgktVcakKqqKMK2CllBLDsjBNiWHacQN100Q3TIq6SdEwyRcNCrqdcgWdfFEnVzTI5otkCzqZfIFM3s7TuSKpXIFUtkAqVyCdLRw0FDsQVRFUBH3EwoGRzqgqEqA6EqA6EqQ6GqAmGqI6EkA7CSPXnhQ3KhRFEAv7iYX9LJxx+HlcuYJOPJ0lkd7fOyczeYYyeZLZPMlsgWQ2TzpXpHMgSSZfJJsvks4VRz0Jx4OqiJHAmYL3RKjFjlJrSmtMUWgPhxAQ8LgJ+NwEvHbnEA34aK6OEvZ77NdBH2G/l2jQO2K1K0J+Qj6PE7H2KJk2ohoPPo+GzxOhoTIy7u/qhkkmXyRX1EcsQ75okNeNkvWwc92wLYluWiNWxrIkZikyrSUlUkpbRKX5ZsOnsKLYIaFVZThSrUArWTvNpaK51BFr6HapeEtW0uvW8Lld+Dy2RfVqrml3vTIVOClFNRE0l0o06COK70Q3xWGScvJclTs4HCccUTk4lBlHVA4OZcYRlYNDmXFE5eBQZiYkKiHETUKILUIISwhxyAdhpXKXCyG2CyF2CiG+MJF9OjicCKSUtA8N8fC2rXz5uWcOW3ait9TfBm4Avj9aASGECnwXuAToANYLIR6RUr4zwX07OBwzhvJ5NvV081ZPNxu7u3mru4uBXA4An+vwspmQqKSUW+GI3pIrgZ1Syt2lsr8ArgUcUTlMCobyebb09bKlt5fNvT1s7ulm79DQyOdzKmKsbpnF6XX1LKuvZ15lFdpffXrU+o7Hw99GoP2A1x3AqJ5nQog7gTsBZsw4vD+Ng8N4kFLSkUyytb+PrX19bO3vZUtvH/tSyZEyDaEQi2tquWnRYk6vrWNxbS1hz/gmBB9RVEKIp4C6Q3z0RSnlw2PYx6HM2Kiz2qSUPwB+APaE2jHU7+DwPhL5HO8ODLC9v5/tA/0jebpYBOyTsiVawdL6em5bsoRF1bUsqqkh5pv4TJkjikpKefEE99EBNB/wugnonGCdDg5IKenJpNk1GGdXfICdg4PsGhxk5+AgfdnMSLmQ28P8qiquX7CQ+VXVnFpdzbzKKvyadkzadTyGf+uBuUKIWcA+4Bbg8HFzHRwOIJ7LsXcowZ5EnNZ4gtZEnNZ4nNZEnKyuj5QLut2cEotx/swW5lVWMreyknmVVdQHg8d1YvGERCWEuB74DlANPCaE2CilvEwI0QDcI6W8UkppCCH+CvgdoAL/JaXcMuGWO0wbCoZBZypFRzJJR3KI9uQQHckkexIJ2oYSJAv7Y/IpQtAYCjOrIsqKxkZmRSuYE4sxpyJGTWByeBFPGydFh8mJYVn0ZzP0pNN0plJ0l/KudIp9ySSdqdRBQzUAl6LQGAoxIxJlRiTKzGiElmgFLdEozeEIniPc0j4eTGsnxTe7OulIJqkOBKjy+6n0+Yl4vSiToMearkgpyeg6g7ks/dn9qTeTpi+ToS+bpSedpieTpj+bxXpPx+1RVRpCYepDIVa3tNAYDtMUjtAUDtMYClMXDKIqU3eyz5QX1QPvbOHnb28+6D1VCKJeH5V+H1Gvl6jXR0Upj3q9RLwewh4vEY+XsMdD2OMh5PEQcrvR1JPHNdy0LDK6TqpQIFkokCra+VA+z1ChwFA+RzyfJ5HPE8/lSOTzDOayDOZyFMxDhySo9PmoDgSoDQSZX2Vfz9QGQ9QGgtSHgtQFQ1R4vZNimHasmPLDv2QhT3c6TV8mS382w2Aux0AuSzxnnwCJfJ54Pkc8lyeRz6EfwR3eo6oE3R6Cbo2A241fcxPQ7HgUAU3D69LwaS68Lhce1YXH5cKjqnhcLtyqOpJcioJLUdAUOzaFq+TNqwiBKuxeWAgQiPe400ukBEsOu9RLzFKsiuGkmxa6ZVI096eCYZAvpYJp5zldJ2cYZHWdrF4kU9TJ6jrpYoGMro/cXh4NAUS8XqJeLxWlDinm81Pp91Hh9VHp94+IaHiUcLJ0StN6+Bf2eAl7vMw78rJBSCnJ6nqpF86TLORJHtBLp4tFUoUC6aJORi+SKRbJ6jrxfI7OVIqsrpM39FJujP6w7QTjVlX8mobX5cLn0vCXOoWYz0dzJELQ7SaguQm63SMWOuTxjFjuiNfeDnk8zjD6KJjyohoPQggCbjcBt5uGUGhCdUkpbQthGhSM/RZj2IIYlkXRNDEtC8OSGJaJJcGSFpYsxag4oK4Dh0NqKSiMWrJsihC4FBWXUopVoSgHWUSPaltJr8u2nI4QTiwnlajKiRDCHvq5XHByhbVzOAJT9xaLg8MkxRGVg0OZcUTl4FBmnGsqB4dxkDeL7Er1HLaMIyoHh0MgpaQnP8TOVDc7U93sSHWxI9VNW6Yf6wgPUxxROZzUSCnpL6RoTffSmu5ld7qHXaWUMfZP5K33VTA3VMfFdYuZG67nQr42ap2OqBxOCgzLZF8uTlumjz2ZPvak+2hN97In00fayI+UC2s+5gRrubz+DOaEajklVMecYC0hbezOi46oHKYNhmXSkx+iIztAe3aAjuwg7Zl+2rL9dGQHMeX+KWqVnhAtgSoubzidlkANs4I1zA7WEHNP3PfKEZXDlEFKScrI05WLsy87SGcuTmdukI7s4MjrA4XjUVw0+6uYHaxldc0iZgarmRmoYmagmvA4LM94cUTlMGnQLYO+fIrewhA9uSF68kN05+N05RJ05xJ05xMHXeeAPVxr8MWYF67nwtrTaPTHaPLHaA5UUe0JoYjj/9TIEdVJRsHU0RR15GQzpUV/IYUAarz2el2d2Tg5s0jQ5aHWFyVrFNgY34NX1VhaMWvcwyPdMhgsZhgopBgopOgfTvkkfYUUfYUkffkhBouZ93035PJS64vS6I9xZmw29b4KGvwVNPgqaPTFCGreCf8m5WbKi2pTfC/7coNEtQARt5+I5ifi9hNQPdPaZ+do6MgO8Pk37+ezp17NGRUtWNJiXf9OnujcSEjzcnXjmTT5K7l31zPU+6JkzSKfnHc5z/e+Q2u6F4+ikTYKnF+z8Ij7+l8b7qM9089AMU1Szx2yTIU7QLUnTJUnxMJwI9XeMNWeMLXeCLW+CLXeKAHX1JtYOeVF9Vjnm6xpX/e+91WhENZ8hFw+wpqPoOYl5PIS1HwEXV4CLs9IHnB58atu/C4PPtWN3+XGp7rxqm48yvRYjTBv6jzUvp7rmpZjWLaDYdYo8mT3Jv7h9JtJG3m+ufVRPjLrfJr9lXx0zmru3fUMO1LdvNq/gy8vuZmCqXP3ljVjEpVf9dASrGGZezYxT5CYO0iVJ0SlJ0S1J0TME0R0YbsAAAANfElEQVRTpvzpd0im/FF9cv7l3NryARLFDEN6lqFiliE9S1LPMqTnSOs5knqepJ6jMxsnbeRIGwWKljGm+hUEHlXDq2p4FM12TFQ03IoLt+JCU1y4FRVNcaEpKi6hoikqqrAdE1Wh2q4bQkFgOyiOrPWLeH9URAkW9tKlFrLkJmJhHpAMy8SQFoYsuZpYBl867Uaibv+ox/HmYCvzwvXkTJ2caUcgUoSgaNq/gyZUipZB1iyOWIeA6iFv6pglx05VKO9zjR+Nfzj95jGVm45MeVEFXV6CLi8zA1Xj+l7RMsgYebJGkYyRJ2MUyJlFMkaBvKmTNe08bxbJmToFUydv6hQtnYJle9cWLZ20kUO3THTLwJC2R64uTczSiT8sCKPkxXukp/EHomD7VSnY/lS2OIcFq6IJteRd7EI/QiexYbAVXZrsSHUR1fysrJyDpqhUecPsyw6SNvI0+yup80Z5LLOBXake9uUGuarxTOaE6nixdxsFS2dJ1IkafCSmvDv9VGRYXKP99sPW7Fjw+663iLoD/L5rE1867Qb2ZQf5SesLeBQXH529mpgnyANtr5IxClR7wlzZuJREMcOa9vW4FRfXN6/APwWvc8rN4dzpHVE5OBwFhxOV4/rh4FBmHFE5OJSZKX+jwsHheJEzhhgs7mWgsPew5RxROTgcgCVNkno38WI78WIH8UIbg0U75c3kkSvAEZXDSYiUFimjj6FiJ4niPhL6PhLFDuLFfQwVO7HY/3jCp0apcDdxSvADVHhmUOmeSYVnBp855JJtNo6oHKYlBTNDUu8mqXczpHeRLHYxpNspqXdjyv1L8KhCI+puJOaewezgKirczXbyNOFTI+PetyMqhymHlJKsmSCl95A2+kjqPaT0XlJ6T2m7h7yVOug7bsVPRGsg5p7J7OAqIloDEXcDUXcjIVc1ooyz2R1ROUwqDKtIxhggYwyW8gHSRj9po4+0XsqN/oMsDYAmvIS0WkJaLXW+BYS1esJaLRGtnoi7Ho8SOm5zOB1RORxzdCtPzhwia8TJmQmyRoKsGSdnJMiYg2SNOFljkIwRp/AeCwP28CzgqiToqqLWt4BTXDWEtGpCrhqCWjVhrfa4iuZITHlR7U2vp7/QilcN4VFDeJUgHjWERw3iUQK4Ff+4THtPbjsv991DxN3A3NAHafYvRQhBUu9hXf9PMWSBlZUfIuaZwYaBX5MxB/EoQVZU3krOTLBu4GcYVoGVlbcRdo9+MTvVkFJiyDwFM0PBylAwU+SttJ2PpORBKWcOkTOTGDJ/yDo14cXviuF3VRDzzKTJv5SAK0bAVVnKqwi6KvGq4UkjmLEw5UW1M/0ybycePUwJgVvx4VYC+NQwt876/mHrk0hU4aZoZQlpNSN/5obBX7Oy8jZciof1Az9neeUfkTL6WFl1G+v77ydrJnhz8AEWRS5HFRqbE4+yqvpPUMTxW1pGSgtT6phSx5BFO7cKmLKIIYvoVh7DKmDIPPpIPpxy6FaOopWjaGVKeba0naVoZrA49JpUw3iUEF41jE8N4XfFqPS04HNF8akRvGoEvxrF54rgVyvwu6JoyrFzaT+RTHlRXVj7ac6rvpO8lSr1mmnyZpKiNdyjZka2pTz8SQFQ653Ptc1fJWcM8WLv97mo/q9RhYuckSCoVaMIlZw5RFLvIazV4lMjRNwNpYvkLqo8cxBCkDJ6j7gvU+o8sPeug96TgMR2tZDSsterwsSSFlKaWJhY0k4SE1MaWNLAlPrI98aP3fFoig9NeHErfjTFR1irwV2y9m41gEcJ4FGCuNXAQSMCnxrGrQSOawcymZnyohJC4Fb9uFU/aLVlqQ/A54pQtLKowv6JXIoHSxooQkUVGn41StZMAJA1EvjUMKpw76/Hdtw44v48ahCJfE9Zxfa3Eqq9KBwKilAQqChCRQgVlVIuXKhCQynlw9su4UYVGi7Fg0t4cAk3LsWDKty2eBQvLuHBrfhQhXtKDa8mO1NeVOVmd+oV9mTWUTDTnF5xLb/v/Ccubfg8Z1Rcz7M9/46UkiUV1xBxN2BaRV7uvQdDFghrdSyOXsWzPf+GBE6NXH7EazlVaFzX/PXjc2AOxw3H9WMUpLQQQsGUxoi10q08Eom7dC2gWzlMaSBQ8KgBe4FpYwALk5Crxun9pzHTennSY8WwlRkWFICmHBy5R1N8aAd9RxDUxueB7DD9cETl4DBGpCyAsRfM1sOWm5CohBA3AX8PLARWSikPOVYTQuwBUoAJGKOZTQeHcvDeNZTH9V0rC2Y7mG1gtiGNNjD32mKyOmEMMUYmaqneBm4ADv/wx+YCKWX/BPfncJIhZRGkAUJFCDs2hrTSoG8GJYjQFiNlDgqvghwCtQXhPgOpb0dm70e4WsB/G+KAO7OHwkr9O+R+AdZ7TlERBVczuJchXDeAOgtcLcDiUeuakKiklFsB54Lc4ZggzW5k+t9BeBCei8FzbklATyH1LQglgpR5UOqQhWcR7uXIwvPgmgGFpxG+68EagOx9ELjjsBZMqI1Iz2qE2gxqs12HOhOhTN5Z6hL4vRBCAt+XUv5gtIJCiDuBOwFmzHDCYZ2sSGlB4XnAQigNMGxpzAFkcR1K5G6k2YtMfwvh/xBCOxXhuwYyPwJ9G9LsQHGfYQuz8MwRnxgK/40IbixL248oKiHEU3BIj6wvSikfHuN+zpVSdgohaoAnhRDbpJQvHKpgSXA/APuW+hjrd5iGSLMb4bnMtlCJuxDuFSA0kEW7gPDA8Gx1WXIslDqIAAzPnhE+xnIdVE6OKCop5cUT3YmUsrOU9woh1gArgUOKavx15wAXQmhHLOtwbJDSApkGawhkspQP2bkVR1pDIBNgxcGycxH4C4T/cJZB2EMxTPt7ImjXo4RBbUYW19n1uJeD2oA0fg65h5FWL0JbhPB8ACv5dbse3012jdPF9UMIEQAUKWWqtH0p8A/lql+mvgHZ+5DCByJkJyUMIghK0M5FEKEE7R5sJPntXkz4D9geTt6yOq1NNuwH/gWQeZA5kNlSPrydBSsLMgMyg5RpsDK2cGQKrFQpT9sikmkOaw2ED0QElApQoqCdCurhn+cJIZDeS5Gpu0F/E+E5F5n+Dkr4S+D/I2T25wglXLoJ4QXv5SALCN+1COFCei9DqDNACYA6p6y/35GY0IwKIcT1wHeAaiABbJRSXiaEaADukVJeKYSYDawpfcUF3C+l/OpY6h/LjApZeBn0jaXeMF36w0t/tJUunQgZ+0QZFxoIbyl5ALedC3dp220PRdBKuauUqyBcpUNVQajYkeCGc1HqMQ9MBx0RYJVO/OFkAlZpSGMCRmnbKA179ANyHSjaQyRZLG0XDkh5oMD4hkRaqZMKHNBxBUt5CESk1GlF7Q5NiZREZAtp+K7ddMKJUAv2DHWZK4ms1Atb2f09syyUhJcHmbeHlQediMMn5/DJqh9w0h54YpulE9ti/8lv2e+PiGQ8KPuTULHF6SoJd3hbK73WSqIv5cINePZ3BsIDeEuWeLjDONBCD1vtgP1asa36kW5Hn4w405SwZ3wjgkBwbOWPUTsOtkDDApPv2eOBFs1hqnHSiGqysH/o5zBdmb5X4w4OJwhHVA4OZcYRlYNDmXFE5eBQZhxROTiUGUdUDg5lxhGVg0OZcUTl4FBmJvU0JSFEH3D4ZeugCpgOHsXT4ThOpmOYKaWsPtQHk1pUY0EI8fp0iHkxHY7DOQYbZ/jn4FBmHFE5OJSZ6SCqUeNdTDGmw3E4x8A0uKZycJhsTAdL5eAwqZhyohJCxIQQTwohdpTyilHK7RFCbBZCbBRCnJhVDt6DEOJyIcR2IcROIcQXDvG5EEL8e+nzTUKIZSeinUdiDMexWggxVPrtNwoh/u5EtHM0hBD/JYToFUK8PcrnE/sfpJRTKgH/DHyhtP0F4J9GKbcHqDrR7T2gPSqwC5gNuIG3gFPfU+ZK4AlsL8azgddOdLuP8jhWA4+e6LYe5hjOB5YBb4/y+YT+hylnqYBrgR+Xtn8MXHcC2zIeVgI7pZS7pZRF4BfYx3Ig1wI/kTavAlEhRP3xbugRGMtxTGqkHXNy8DBFJvQ/TEVR1UopuwBKec0o5Yaj4r5Rinp7omkE2g943VF6b7xlTjRjbeMqIcRbQognhBCLjk/TysaE/odJGaPicFFxx1HNmKPiHicOFZjivbdex1LmRDOWNm7AnsaTFkJcCTwEzD3mLSsfE/ofJqWo5GGi4goheoQQ9VLKrpJJPuSK1fIYRsU9SjqA5gNeNwGdR1HmRHPENkopkwdsPy6E+E8hRJWcOqu+TOh/mIrDv0eA20vbtwPvi+cuhAgIIULD29hRcQ95p+c4sh6YK4SYJexAerdgH8uBPAJ8pHT36WxgaHioO4k44nEIIepEKb6aEGIl9nk2cNxbevRM7H840XdijuLOTSXwNLCjlMdK7zcAj5e2Z2PflXoL2IK9mMJkaPuVwLvYd8++WHrvY8DHStsC+G7p883A8hPd5qM8jr8q/e5vAa8C55zoNr+n/T8HugAd2yrdUc7/wZlR4eBQZqbi8M/BYVLjiMrBocw4onJwKDOOqBwcyowjKgeHMuOIysGhzDiicnAoM46oHBzKzP8HEfVKQyAS+k8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output(AdamOptimizer([w], lr=0.1, alpha=0.7, momentum=0.7), nsteps=30, noise=1.0, fname=\"adam_noise_example.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Final Optimization.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
